Question

A kids rocket is fired from rest from the ground (y=0) at time t₁=0s. As the rocket fuel is burning its fuel it moves vertically upward with constant acceleation of +4.25m/s². At t₂=12s all fuel is used up and rocket is in freefall and air resistance can be neglected in this case.

what is the maximum height of rocket with respect to ground? Also how long after being launched does the rocket return to the ground? And what is the velocity of the rocket the moment before it hits the grounf?

Answer 1

0 to 12s:

d1 = v0 t + a t^2 / 2

h1 = 0 + (4.25 x 12^2 / 2) = 306 m

and v = v0 + a t

v1 = 0 + (4.25 x 12 ) = 51 m/s upward

after that rocket will be in free fall.

at maxi height v = 0

vf^2 - vi^2 = 2 a d

0^2 - 51^2 = 2(-9.8)(h2)

h2 = 132.7 m

Maximum height = h1 + h2 = 438.7 m ........Ans

yf - yi = vo t + a t^2 /2

0 - 306 = 51 t - 9.8 t^2 /2

4.9 t^2 - 51 t - 306 = 0

t =14.7 sec  

total time = 14.7 + 12 = 26.7 sec ......Ans

vf = vi + a t

v = 51 + (-9.8 x 14.7)

v = - 93 m /s

final velocity = 93 m/s downward