Projectile problem: a 7500-kg rocket blasts off vertically from the launch pad with a constant upward acceleration of 2.25 m/s2 and feels no appreciable air resistance. when it has reached a height of 525 m, its engines suddenly fail so that the only force acting on it is now gravity.

a) what is the maximum height this rocket will reach above the launch pad?
b) how much time after engine failure will elapse before the rocket comes crashing down to the launch pad?

Here, 

height at failure, h1 = 525 m, 
upward acceleration, a = 2.25 m/s^2, 
velocity = v m/s, 

SO, 

v^2 = 2*a*h = 2*2.25*525 = 2362.5 
Now, acceleration, g = 9.8 m/s^2, 

SO, 

heigt, h1 = v^2/2g = 2362.5 / 2*9.8 = 120.54 meters 
Hence, 

a) 
Total height = 525+120.54 = 645.54 meters 

b) 
time, for h1, t = v/g = sqrt(2362.5)/9.8 = 4.96 sec 



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Height at failure, h1 = 525 m, 
upward acceleration, a = 2.25 m/s^2, 
velocity = v m/s, 

SO, 

v^2 = 2*a*h = 2*2.25*525 = 2362.5 
Now, acceleration, g = 9.8 m/s^2, 

SO, 

heigt, h1 = v^2/2g = 2362.5 / 2*9.8 = 120.54 meters 
Hence, 

a) 
Total height = 525+120.54 = 645.54 meters 

b) 
time, for h1, t = v/g = sqrt(2362.5)/9.8 = 4.96 sec 

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