calculus
posted by jessica .
Consider a gun fired from a tower 96ft above the ground. The angle of elevation of the gun is 60 degrees, and its muzzle velocity is 1600 ft/sec (also gravity in this equation is 32 ft/sec^2).
a)When does the bullet hit the ground?
b)Write a parametric equation that models the path of the bullet.
c)What is the range of the gun?
d) find the equation for the bullet based on rectangular coordinates. What type of curve is this?

x = u t
y = yi + vi t  16 t^2

u = 1600 cos 60 = 800 ft/sec the whole time
so
x = u t
vi = 1600 sin 60 = 1386 ft/s
so
y = 96 + 1386 t 16 t^2
so
when is y = 0 ?
0 = 96 + 1386 t  16 t^2
16 t^2  1386 t  96 = 0
so
t = 86.7 or .07 (forget negative root)
so hits ground in 86.7 seconds
do u t for range
for part d use t = x/u, u is constant
y = yi + vi (x/u)  16 x^2/u^2
or
y = c + b x + a x^2 a parabola
Respond to this Question
Similar Questions

physics problemgun (projectile problem)
A gun shoots bullets that leave the muzzle at 250 m/s. If a bullet is tohit a target 160.8 m away at the level of the muzzle, the gun must be aimedat a point above the target. (Neglect air resistance.) How far above the target is this … 
physics
The citizens of Paris were terrified during World War I when they were suddenly bombarded with shells fired from a longrange gun known as Big Bertha. The barrel of the gun was 36.6 m long and it had a muzzle speed of 1.48 km/s. When … 
Physics
A handpumped water gun is held level at a height of 0.85 m above the ground and fired. The water stream from the gun hits the ground a horizontal distance of 6.9 m from the muzzle. Find the gauge pressure of the water gun's reservoir … 
physics
A pistol is fired horizontally and the bullet has a muzzle velocity (speed with which the bullet leaves the barrel) of 31.3 m/s. The gun is 50 m above the surrounding terrain. a) How far away does the bullet land measured horizontally … 
Physics
A railroad gun of mass M = 3.0 kg fires a shell of mass m=1.0 kg at an angle of θ= 45.0 ∘ with respect to the horizontal as measured relative to the gun. After the firing is complete, the final speed of the projectile relative … 
Physics
A railroad gun of mass M = 3.0 kg fires a shell of mass m=1.0 kg at an angle of θ= 45.0 ∘ with respect to the horizontal as measured relative to the gun. After the firing is complete, the final speed of the projectile relative … 
Physics ASAP PLease
A railroad gun of mass M = 2.0 kg fires a shell of mass m =1.0 kg at an angle of theta= 35.0 with respect to the horizontal as measured relative to the gun. After the firing is complete, the final speed of the projectile relative to … 
Physics Classical Mechanics
A railroad gun of mass M = 2.0 kg fires a shell of mass m=1.0 kg at an angle of θ= 40.0 ∘ with respect to the horizontal as measured relative to the gun. After the firing is complete, the final speed of the projectile relative … 
physics
A railroad gun of mass M = 2.0 kg fires a shell of mass m =1.0 kg at an angle of theta= 35.0 with respect to the horizontal as measured relative to the gun. After the firing is complete, the final speed of the projectile relative to … 
pre calculus
a gun with a muzzle velocity of 1200 feet per second is fired at an angle of 6 degrees above the horizontal. find the component form of a vector. verify the magnitude