Question

launch an 950 g model rocket straight up and hit a horizontally moving target as it passes 33.0 m above the launch point. The rocket engine provides a constant thrust of 20.0 N . The target is approaching at a speed of 18.0.At what horizontal distance between the target and the rocket should you launch?

Answer 1

Answer:

$s=43.6124\ m$ is the horizontal distance between the rocket and the target when the rocket should be launched.

Explanation:

Given:

• mass of rocket, $m=0.95\ kg$

• height of horizontal moving target, $h=33\ m$

• constant thrust of rocket, $F=20\ N$

• speed of approach of the target, $v_h=18\ m.s^{-1}$

Now the acceleration of the rocket:

$a=\frac{F}{m}$

$a=\frac{20}{0.95}$

$a=21.052\ m.s^{-2}$

Since this acceleration is acting against the gravity therefore there will be a lesser effective acceleration of the rocket:

$a'=a-g$

$a'=21.052-9.81$

$a'=11.242\ m.s^{-2}$

Now the time taken by the rocket to reach the height of 33 m:

$h=u.t+\frac{1}{2} \times g.t^2$

where:

$u=$ initial velocity of the rocket $=0\ m.s^{-1}$

$33=0+0.5\times 11.242\times t^2$

$t=2.4229\ s$

Now the distance covered by the target in the above time when the rocket has reached the  height of the target:

$s=v_h.t$

$s=18\times 2.4229$

$s=43.6124\ m$ is the horizontal distance between the rocket and the target when the rocket should be launched.