# science

prove that the maximum horizontal range is 4 times the maximum height attained by a projectile which is fired long the required oblique direction

1. 👍 1
2. 👎 0
3. 👁 1,085
1. The maximum range is achieved when θ=π/4

R = v^2 sin2θ/g
h = v^2 sin^2 θ / 2g

R/h = 4cotθ

at θ=π/4, R/h = 4

1. 👍 1
2. 👎 1

## Similar Questions

1. ### pysics

A projectile of mass 0.777 kg is shot from a cannon, at height 6.6 m, as shown in the ﬁgure, with an initial velocity vi having a horizontal component of 7.8m/s. The projectile rises to a maximum height of ∆y above the end of

2. ### physics

A projectile is fired with an initial speed of 65.2 m/s at an angle of 34.5 degree above the horizontal on a long flat firing range. Determine (a) The maximum height reached by the projectile, (b) The total time in the air, (c)

3. ### pre-calc

analyzing the motion of a projectile: a projectile is fired from a cliff 200 feet above the water at an inclination of 45 degrees, with a muzzle velocity of 50 feet per second. the height of the projectile above the water is given

4. ### Science

A projectile has a range of 50m and reaches a maximum height of 10m. Calculate the angle at which the projectile is fired.

1. ### Physics

A projectile is shot on level ground with a horizontal velocity of 21 m/s and a vertical velocity of 45 m/s. Part 1) Find the time the projectile is in the air. The acceleration due to gravity is 9.8 m/s^2 .Answer in units of s.

2. ### 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

3. ### Algebra

A projectile is launched upward with a velocity of 128 feet per second from the top of a 50- foot platform. What is the maximum height attained by the projectile?

4. ### Physics

The speed of a projectile when it reaches its maximum height is 0.42 times its speed when it is at half its maximum height. What is the initial projection angle of the projectile?

1. ### physics

A stone is thrown horizontally outward from the top of a bridge, the stone is released 19.6meter above the street below.the initial velocity of the stone is 5.0m/s.determine the (a)total time that the stone is in the air

2. ### 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?

3. ### math

The maximum, range of a projectile is directly proportional to the square of its velocity. A baseball pitcher throws a ball at 60 mph, with a maximum range of 242 ft. What is his maximum range if he throws the ball at 70 mph?

4. ### Pre-Calculus

1. A projectile is fired straight up from a height of 6 feet. Its height (h) in feet after t seconds is given by h = 6 + 192t -16t^2. Answer: h = -16t^2 + 192t + 6 h = -16( t^2 -12t +36) + 6 +576 h = -16 (t-6)^2 +582 The maximum