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July 29, 2014

Search: A projectile is fired at an upward angle of 40.0 from the top of a 265- cliff with a speed of 145

Number of results: 15,573

Math
A projectile is fired upward 200 ft from an observer. The height in feet of the projectile after t seconds is given by s=-16t2 + 180t. What is the rate of change of the angle of elevation of the observer to the projectile after 7 seconds? I don't understand how to get there!
April 2, 2012 by Linda

Physics
A projectile is fired such that its horizontal range is equal to 2.5 times its maximum height. Find the angle the projectile was fired at
March 2, 2014 by Yera

physics
a projectile with a muzzle velocity of 550 m/s is fired from the a gun on top of a cliff 460 m above the sea level at a certain angle with respect to the horizontal. if the projectile hits the ocean surface. 49.2 seconds after being fired, determine the horizontal range of the...
May 4, 2013 by jennierson

physics
A projectile was fired out of a lead ejector at an angle of 45 degrees up from horizontal. The projectile velocity was 1000.00 meters per second. How high did it go? and how far did the projectile go?
May 2, 2013 by john

Physics (last question)
A 800 kg projectile is fired vertically upward with an intitial velocity of 50 m/s. Assuming that no friction is present, how high above the ground will the projectile travel?
November 15, 2007 by Elizabeth

math
A projectile is fired directly upward with a muzzle velocity of 860 feet per second from a height of 7 feet above the ground. a. Determine a function for the height of the projectile t seconds after its released. b. How long does it take the projectile to reach of height of ...
March 7, 2010 by bill

Physics
Q Exactly 2.7s after a projectile is fired into the air from the ground ,it is observed to have a velocity v = (8.8i+4.5 j) m/s where the x-axis is horizontal and the y axis is positive upward . a)Determine the horizontal range of the projectile b)Determine the maximum height ...
September 1, 2012 by Nikitha

physics
A projectile is fired at an upward angle of 45 degrees from the top of a 265 m cliff with a speed of 350 m/s. What will be it's speed when it strikes the ground below?
October 26, 2010 by jessica

physics
a projectile is fired from the top of a building with an initial velocity straight upward at 40m/sec. the top of the building is 50 meters above the ground? a) the maximun height of the projectile above the building b) the time for the projectile to reach the top c) the ...
October 15, 2011 by daniel

Math
A projectile is fired with an initial velocity of v0 feet per second. The projectile can be pictured as being fired from the origin into the first quadrant, making an angle O with the positive x-axis. If there is no air resistance, then at t seconds the coordinates of the ...
September 8, 2013 by Sarah

Physics
A projectile is fired with an initial velocity of v0 feet per second. The projectile can be pictured as being fired from the origin into the first quadrant, making an angle O with the positive x-axis. If there is no air resistance, then at t seconds the coordinates of the ...
September 8, 2013 by miley

PHYSICS
A Projectile IS FIRED FROM THE TOP OF A BUILDING WITH AN INITIAL VELOCITY STRAIGH UPWARD AT 40.0 M/SEC . THE TOP OF THE BUILDING IS 50.0 METERS ABOVE THE GROUND. A) THE MAXIMUN HEIGHT OF THE PROJECTILE ABOVE THE BUILDING. B) THE TIME FOR THE PROJECTILE TO REACH THE TOP. C) THE...
October 16, 2011 by HELPPMEEEEEEEEEE

physics
A projectile is fired at an angle of 30ᵒ above the horizontal from the top of the cliff 600 ft high. The initial speed of the projectile is 2000 ft/s. how far will the projectile move horizontally before it hits the level ground at the base of the cliff?
January 13, 2014 by Anonymous

Physics
A projectile is fired at an upward angle of 25.0^\circ from the top of a 310 m cliff with a speed of 220 m/s. What will be its speed when it strikes the ground below? (Use conservation of energy.)
November 15, 2010 by Linda

Physics
A projectile is fired from ground level with a speed of 40 m/s at an angle of 30 degrees and hits a building 100m away. What is the time of flight of the projectile? How high above ground does the projectile hit the building? What is the speed of the projectile just before it ...
February 5, 2012 by Krystal

College Physics
A projectile is fired at an upward angle of 55.0 degrees from the top of a 230m cliff with a speed of 180m/s.What will be its speed when it strikes the ground below? (Use conservation of energy.)
February 25, 2010 by Sandy

physics
A 3Kg projectile is fired straight upward from earth's surface with a speed that is one-fourth the escape speed. Neglecting air resistance. a) What is the Kinetic energy of this projectile when it is launched? b) what is the gravitational potential energy of this projectile ...
February 14, 2011 by rick

Math
A projectile is fired straight up from a cliff which is 200 feet above ground with an initial velocity of 220 ft/sec. Assume that the only force affecting the projectile during flight is from gravity which produces a downward acceleration 32 ft/sec^2. Find an equation from the...
December 8, 2010 by Marina

Physics
A projectile is fired straight up from a cliff which is 200 feet above ground with an initial velocity of 220 ft/sec. Assume that the only force affecting the projectile during flight is from gravity which produces a downward acceleration 32 ft/sec^2. Find an equation from the...
December 8, 2010 by Marina

Physics
a projectile is fired with an initial speed of 53 m/s. Find the angle of projection such that the maximum height of the projectile is equal to its horizontal range
September 23, 2012 by Amanda and Travis

Math
A projectile is fired with an initial velocity of 350 feet per second at an angle of 45 with the horizontal. To the nearest foot, find the maximum altitude of the projectile. The parametric equations for the path of the projectile are x = (350 cos 45)t, and y = (350 sin 45)...
April 12, 2008 by Devon

physics
A projectile is fired with velocity v at angle thita. Find the time when velocity of projectile will make angle 90' with initial direction of velocity?
July 25, 2011 by Shivam

physics
A projectile is fired with velocity v at angle thita. Find the time when velocity of projectile will make angle 90' with initial direction of velocity?
July 25, 2011 by Shivam

physics
a projectile is fired from the surface of the earth with a speed of 200 m/s at an angle of 30 degrees above the horizontal. If the ground is level, what is the maximum height reached by the projectile
September 25, 2011 by Anonymous

physics
if a ball, fired as a projectile, travels 30 meters when it leaves the the ground at 20% angel, it will travel the same distance when fired at an angle of what degrees
November 19, 2010 by luke

physics
if a ball, fired as a projectile, travels 30 meters when it leaves the the ground at 20% angel, it will travel the same distance when fired at an angle of what degrees
November 19, 2010 by luke

Applying Algebraic Thinking to Data
Snoopy is in his plane, 4500 ft above ground. he fires a projectile straight up. The Vo of the projectile is 340 ft/s. (after the projectile is fired, it has no acceleration, so its height can be modeled by a "falling body" model). The Red baron is maintaining a constant ...
April 20, 2012 by Rachelle

physics
Consider a projectile fired horizontally from a cliff of a given height. With what speed must it be fired so that it makes a 45 degree angle with the ground when it hits
September 24, 2010 by Ligu

physics
A projectile is fired from the ground level with initial velocity of 90m/s at an angle of 36degre from horizontal. find the magnitude and direct of projectile 5 secs after firring
February 6, 2010 by Anonymous

physics
A projectile is fired from the ground level with initial velocity of 90m/s at an angle of 36degre from horizontal. find the magnitude and direct of projectile 5 secs after firring
February 6, 2010 by Anonymous

physics
A projectile is launched from ground level to the top of a cliff which is 195 m away and 155 m high. If the projectile lands on top of the cliff 9.2 s after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect air resistance. Calculate ...
September 22, 2010 by Sam

Physics please help!!
A projectile is fired at 45.0 above the horizontal. Its initial speed is equal to 42.5 m/s. Assume that the free-fall acceleration is constant throughout and that the effects of the air can be ignored. What is the maximum height reached by the projectile? At what time after ...
February 3, 2013 by Julia

Physics
A projectile is launched from ground level to the top of a cliff which is 195 m away and 155 m high. If the projectile lands on top of the cliff 9.2 s after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect air resistance. Also ...
September 23, 2010 by Sam

AP PYHSICS
A projectile is fired from the surface of the Earth with a speed of 150 meters per second at an angle of 45 degrees above the horizontal. If the ground is level, what is the maximum height reached by the projectile?
October 1, 2012 by Liz

PHYSICS
A projectile is fired from the surface of the Earth with a speed of 150 meters per second at an angle of 45 degrees above the horizontal. If the ground is level, what is the maximum height reached by the projectile?
October 1, 2012 by Liz

Intermediate Algebra
If a projectile is fired straight upward from the ground with an inital speed of 96 feet per second, then its height (h) in feet after t seconds is given by the equation h(t)=-16t^2+96t Find the maximum height of the projectile.
April 22, 2012 by Ralph

Physics
The projectile motion is fired with velocity of magnitude vo at the angle feta. Find feta for which the maximum elevation of the projectile is twice its range
September 22, 2011 by Whitney

Physics
The projectile motion is fired with velocity of magnitude vo at the angle feta. Find feta for which the maximum elevation of the projectile is twice its range
September 22, 2011 by Whitney

projectile motion
A missile is fired upwards from the top of a cliff in a direction making an angle (not known ) with the horizontal. After 20seconds the projectile hits the ground at a point which is 1800metre from the foot of the tower of height 160metres. Find the angle of projection and the...
June 16, 2014 by tanaiah

math
A gun is fired from a bunker of 2m deep with an initial velocity of 500m/s at an angle of pi/6 a) Find the parametric equations of the position of the projectile b) Find the range of the projectile to the nearest meter. c) Find the maximum height of the projectile to the ...
March 17, 2011 by Sandy

Physics
A projectile is fired at v0 = 394.0 m/s at an angle of θ = 68.7o with respect to the horizontal. Assume that air friction will shorten the range by 28.1%. How far will the projectile travel in the horizontal direction, R?
December 2, 2012 by Mike

Physics
A projectile is fired at 65.0 above the horizontal. Its initial speed is equal to 37.5 m/s. Assume that the free-fall acceleration is constant throughout and that the effects of the air can be ignored.At what time after being fired does the projectile reach this maximum height?
February 8, 2013 by Anonymous

Science - Physics
When a projectile is fired horizontally, which of the components of its motion is (A) motion at constatnt speed (B) uniformly accelerated motion (C) If the initial velocity of the projectile is increased, what effect will this have on the time it takes the projectile to fall ...
December 6, 2006 by Nicole

Physics
A projectile is fired from the surface of the Earth with a speed of 200 meters per second at an angle of 30 above the horizontal. If the ground is level, what is the maximum height reached by the projectile? (A) 5 m (B) 10 m (C) 500 m (D) 1,000 m (E) 2,000 m
October 12, 2013 by Mehrin Ali

Physics
A projectile is fired from the surface of the Earth with a speed of 200 meters per second at an angle of 30 above the horizontal. If the ground is level, what is the maximum height reached by the projectile? (A) 5 m (B) 10 m (C) 500 m (D) 1,000 m (E) 2,000 m
October 12, 2013 by Mehrin Ali

Physics
A projectile is fired from the surface of the Earth with a speed of 200 meters per second at an angle of 30 above the horizontal. If the ground is level, what is the maximum height reached by the projectile? (A) 5 m (B) 10 m (C) 500 m (D) 1,000 m (E) 2,000 m
October 12, 2013 by Mehrin Ali

Physics
A projectile is fired with a speed of 50 m/s at an angle of 37 find the horizontal and vertical components of its velocity find the time that the projectile will spend in the air find the distance downfield that it will travel
November 22, 2008 by IDK

AP Physics - Work and Energy
A projectile is fired at an upward angle of 45 degrees from the top of a 265-m cliff with a speed of 185 m/s. What will be its speed when strikes the ground below? (Use conservation of energy.) I have a diagram of it but I don't know what equations to use. Help?
October 15, 2009 by Henry

Physics
A projectile is fired with an initial speed of 31.0 at an angle of 10.0 above the horizontal. The object hits the ground 7.50 later. a. How much higher or lower is the launch point relative to the point where the projectile hits the ground? b. To what maximum height above the ...
October 15, 2009 by Kelcie

Physics
A projectile is fired with an initial speed of 28.0 m/s at an angle of 65 degrees above the horizontal. The object hits the ground 9.5 seconds later. a) How much higher or lower is the launch point relative to the point where the projectile hits the ground? b) To what maximum ...
October 19, 2011 by Sara

college alg
The height of a projectile fired upward is given by the formula s = v0t − 16t2, where s is the height, v0 is the initial velocity, and t is the time. Find the time for a projectile to return to Earth if it has an initial velocity of 184 ft/s.
April 8, 2014 by kmill

college alg.
The height of a projectile fired upward is given by the formula s = v0t − 16t2, where s is the height, v0 is the initial velocity, and t is the time. Find the time for a projectile to return to Earth if it has an initial velocity of 184 ft/s. ____________ s
April 8, 2014 by Kmil

AP Calculus
A projectile fired upward from ground level is to reach a maximum height of 1,600 feet. What is its initial velocity?
September 11, 2013 by Sarah

physics
A projectile fired vertically up from a cannon rises 200 m before returning to the ground. If the same cannon were to fire the same projectile at an angle 45 degrees, then the maximum rangerange would be m.
December 15, 2010 by mc

physics
A projectile fired vertically up from a cannon rises 200 m before returning to the ground. If the same cannon were to fire the same projectile at an angle 45 degrees, then the maximum range would be m.
December 15, 2010 by mc

precalculus
If a projectile is fired with velocity v0 at an angle θ, then its range, the horizontal distance it travels (in feet), is modeled by the function R(θ) = v02 sin 2θ 32 . If v0 = 2600 ft/s, what angle (in degrees) should be chosen for the projectile to hit a ...
October 28, 2012 by Ama

physics HELP
A projectile is fired with an initial speed of 1000 m/s at an angle of 37 degrees above the horizontal. If air resistance is neglected, the horizontal component of the projectile's velocity after 20 s is approximately A) 600 m/s B) 800 m/s C) 640 m/s D) 40 m/s E) 160 m/s ...
November 30, 2010 by anonymous

physics
Suppose we attempt to account for air resistance in our projectile motion in the following (incorrect) way: we alter g so that the acceleration in the y direction is -8 m/s2, and introduce a horizontal acceleration of -3 m/s2. With these changes, find the landing point of a ...
September 2, 2012 by mitch

physics
A projectile is fired into the air from the top of a cliff of height h = 208 m above a valley. Its initial velocity is v0 = 55.2 m/s at an angle θ = 54 above the horizontal. Where does the projectile land? (Ignore any effects due to air resistance.)
February 12, 2014 by John

physics
A spherical non-rotating planet (with no atmosphere) has mass 4 kg and radius 9000 km. A projectile of mass is fired from the surface of the planet at a point with a speed at an angle with respect to the radial direction. In its subsequent trajectory the projectile reaches a ...
December 6, 2013 by juanpro

math
The height of a projectile fired upward is given by the formula s = v0t − 16t2, where s is the height in feet, v0 is the initial velocity, and t is the time in seconds. Find the time for a projectile to reach a height of 96 ft if it has an initial velocity of 128 ft/s. ...
July 11, 2011 by sabrina

Physics
A projectile is fired at an angle of 60degree with the horizontal and with the initial velocity 80m/s calculate (a) the time of flight(b)time to reach maximum height(c)it range(d)the velocity of projection 2seconds after been fired
October 5, 2010 by Sugarkanpaw

physics
a projectile is fired at an angle of 60 degrees with the horizontal and with the initital velocity of 80 m/s. What is the time of flight? What is the max height attained and the time taken to attain it? What is the range? The velocity of projection 2 seconds after being fired?
April 12, 2012 by Anonymous

Physics
In the absence of air resistance, a projectile is launched from and returns to ground level. It follows a trajectory similar to that in the figure below and has a range of 15 m. Suppose the launch speed is doubled, and the projectile is fired at the same angle above the ground...
September 18, 2012 by Anonymous

Physics
In the absence of air resistance, a projectile is launched from and returns to ground level. It follows a trajectory similar to that shown in Figure 3.10 and has a range of 24 m. Suppose the launch speed is doubled, and the projectile is fired at the same angle above the ...
September 7, 2013 by WR

PHYSICS!
A projectile is fired with an initial speed of 32.5 m/s at an angle of 61.4 above the horizontal. The object hits the ground 7.55 s later. What is the absolute value of the difference in height between the launch point and the point where the projectile hits the ground?
February 14, 2009 by JJ

PHYSICS!
A projectile is fired with an initial speed of 32.5 m/s at an angle of 61.4 above the horizontal. The object hits the ground 7.55 s later. What is the absolute value of the difference in height between the launch point and the point where the projectile hits the ground?
February 14, 2009 by JJ

Physics
A projectile is launched at an angle of 34.0o above the horizontal. The projectile has a mass of 1.50 kg and is given an initial speed of 20.0 m/s. a) What is the initial kinetic energy of the projectile? b) By how much does the gravitational potential energy of the projectile...
May 30, 2014 by John

physics i really need help :(
A projectile is fired with an initial speed of 61.3m/s at an angle of 31.5 above the horizontal on a long flat firing range. a)Determine the maximum height reached by the projectile. b)Determine the total time in the air. c)Determine the total horizontal distance covered (...
November 24, 2012 by juanita

Physics
A projectile is fired up into the air at a speed of 164 m/s at an angle of 37 relative to the horizontal. Ignore air drag. A.) Determine the MAXIMUM HEIGHT (above where it was thrown) the projectile will reach. m B.) Determine how LONG the projectile will be in the air. ...
September 6, 2012 by Cindy

college algebra
The height of a projectile fired upward is given by the formula s = v0t 16t2, where s is the height, v0 is the initial velocity and t is the time. Find the times at which a projectile with an initial velocity of 128 ft/s will be 144 ft above the ground. Round to the nearest ...
April 8, 2014 by Kelly

physics
a projectile is fired at an angle of 60 degrees with the horizontal and with the initital velocity of 80 m/s. What is the time of flight?
April 12, 2012 by Anonymous

Phsyics
A projectile is fired with an initial speed of 61.3m/s at an angle of 44.2∘ above the horizontal on a long flat firing range. (a) Determine the maximum height reached by the projectile. (b) Determine the total time in the air. (c) Determine the total horizontal distance ...
September 15, 2013 by Tucker

science
A projectile is fired with an initial speed of 120m.s' at an angle of 60' above the horizontal from the top of a 50m high cliff. (a) determine the maximum height(above the cliff) reached by the projectile (b) how long it takes to fall to the ground from the max. height?. ...
February 9, 2011 by Mykmoloko

science
A projectile is fired with an initial speed of 120m.s' at an angle of 60' above the horizontal from the top of a 50m high cliff. (a) determine the maximum height(above the cliff) reached by the projectile (b) how long it takes to fall to the ground from the max. height?. ...
February 9, 2011 by Mykmoloko

mit physics
A spherical non-rotating planet (with no atmosphere) has mass m 1= 6 10 24 kg and radius r 1= 9000 km. A projectile of mass m 2≪ m 1 is fired from the surface of the planet at a point A with a speed v A at an angle α=30 ∘ with respect to the radial direction...
December 6, 2013 by juanpro

physics
A 0.25 kg skeet (clay target) is fired at an angle of 30 degrees to the horizon with a speed of 25 m/s. When it reaches the maximum height, it is hit from below by a 15 g pellet travelling upward at a speed of 200 m/s. The pellet is embedded in the skeet. (a) How much higher ...
August 19, 2010 by riley

physical science
A projectile is launched upward at an angle of 75 from the horizontal and strikes the ground a certain distance away. For what other angle would it have the same range?
February 9, 2011 by Mykmoloko

physics help
A spherical non-rotating planet (with no atmosphere) has mass m1= 5 1024 kg and radius r1= 8000 km. A projectile of mass m2≪m1 is fired from the surface of the planet at a point A with a speed vA at an angle α=30∘ with respect to the radial direction. In its ...
December 8, 2013 by Anonymous

physics
A projectile is fired from the origin (at y = 0 m) as shown in the diagram. The initial velocity components are V0x = 310 m/s and V0y = 26 m/s. The projectile reaches maximum height at point P, then it falls and strikes the ground at point Q, which is 20 m below the launch ...
February 21, 2013 by Anonymous

physics
A projectile is fired with an initial speed of 26.0 m/s at an angle of 30.0 above the horizontal. the object hits the ground 9.00 s later
October 5, 2011 by Anonymous

Classical Mechanics Physics
A spherical non-rotating planet (with no atmosphere) has mass m1= 3 1024 kg and radius r1= 8000 km. A projectile of mass m2≪m1 is fired from the surface of the planet at a point A with a speed vA at an angle α=30∘ with respect to the radial direction. In its ...
December 6, 2013 by Anonymous

Physics Classical Mechanics
A spherical non-rotating planet (with no atmosphere) has mass m1= 4 1024 kg and radius r1= 5000 km. A projectile of mass m2≪m1 is fired from the surface of the planet at a point A with a speed vA at an angle α=30∘ with respect to the radial direction. In its ...
December 8, 2013 by Mary

math
A projectile is launched from ground level to the top of a cliff which is 195m away and 135m high. If the projectile lands on top of the cliff 6.9s after it is fired, find the initial velocity of the projectile ((a)magnitude and (b)direction. Neglect air resistance.
September 12, 2009 by Cassandra

Physics
A projectile is launched from ground level to the top of a cliff which is 195 m away and 155 m high. If the projectile lands on top of the cliff 9.2 s after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect air resistance.
September 21, 2010 by Jamie

physics
A projectile is launched from ground level to the top of a cliff which is 195 m away and 135 m high.If the projectile lands on top of the cliff 6.5 s after it is fired, find the initial velocity of the projectile ( (a)magnitude and (b)direction ). Neglect air resistance.
November 9, 2010 by bobjahng2

physics
A projectile is launched from ground level to the top of a cliff which is 195 m away and 135 m high.If the projectile lands on top of the cliff 6.5 s after it is fired, find the initial velocity of the projectile ( (a)magnitude and (b)direction ). Neglect air resistance.
November 11, 2010 by bobjahng2

Dynamics
Fundamental Problem 15.12 The cannon and support without a projectile have a mass of 250 kg. If a 20 kg projectile is fired from the cannon with a velocity of 400 m/s , measured relative to the cannon, determine the speed of the projectile as it leaves the barrel of the cannon...
September 21, 2011 by Kate

Physics
A projectile is fired off a 35m cliff at 18m/s. what horizontal distance does the projectile travel before hitting the ground?
October 10, 2013 by Miranda

physics
The path of a projectile fired at a 30 degree angle to the horizontal is best described as 1.parabolic 2.linear 3.circular 4.hyperbolic
October 29, 2007 by lin

physics
A projectile is fired in such a way that its horizontal range is equal to 8.5 times its maximum height. What is the angle of projection?
February 18, 2011 by eric

Physics
A projectile is fired in such a way that its horizontal range is equal to 2.6 times its maximum height, what is the angle of projection?
February 5, 2012 by Boone

Physics
A projectile is fired from ground level with an initial velocity of 50m/s and an initial angle of 30degree. Assuming g= 9.8 m/s*2, find: (a) The projectile total time of flight. (b) The maximum height attained (c) The total horizontal traveled (d) The final horizontal and ...
September 24, 2012 by Abraham

Physics
A projectile is launched from ground level to the top of a cliff which is 195m away and 135m high (as shown in the figure ).If the projectile lands on top of the cliff 6.9s after it is fired, find the initial velocity of the projectile a)magnitude b)direction Neglect air ...
September 12, 2009 by Jannie

science
The projectile is fired at an angle of 45 degree to the horizontal with an initial speed of 100 feet per second. Show work.
March 14, 2011 by kasey kim

calculus
a projectile is fired upward from the ground to reach 64 feet. What is the velocity when it is 48 feet above the ground
April 17, 2012 by jackie

Houston community college
A projectile is fired from ground level with an initial velocity of 50m/s and an initial angle of 30degree. Assuming g= 9.8 m/s*2, find: (a) The projectile total time of flight. (b) The maximum height attained (c) The total horizontal traveled (d) The final horizontal and ...
September 24, 2012 by Abraham

physics(URGENT!!!!!)
A spherical non-rotating planet (with no atmosphere) has mass m1= 5 ×1024 kg and radius r1= 7000 km. A projectile of mass m2≪m1 is fired from the surface of the planet at a point A with a speed vA at an angle α=30∘ with respect to the radial direction. In...
December 8, 2013 by Anonimus

Physics
A catapult throws a projectile at a 40.0 angle with a velocity of 26.0 m/s. How high will the projectile reach, and how far away will the projectile land?
December 18, 2010 by George

Physics
The highest barrier that a projectile can clear is 14.5 m, when the projectile is launched at an angle of 31.0 above the horizontal. What is the projectile's launch speed?
October 15, 2011 by Heather

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