Answer to Question #347061 in Physics for ann

Question

A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 74.3 m/s² for 1.80 seconds, at which point its fuel abruptly runs out. Air resistance has no effect on its flight. What maximum altitude (above the ground) will the rocket reach?

Answer 1

Given:

$v_0=0, \; a=74.3\:{\rm m/s},\; t=1.80\:\rm s$

$$h=h_1+h_2=v_0t+at^2/2+\frac{v_1^2}{2g}$$ $$v_1=v_0+at=at$$

Hence, the maximum altitude that the rocket will reach

$$h=at^2/2+\frac{(at)^2}{2g}$$

$$h=74.3*1.80^2/2+(74.3*1.80)^2/(2*9.81)\\ =1032\:\rm m$$