Question

A model rocket is launched straight upward with an initial speed of 56.5 m/s. It accelerates with a constant upward acceleration of 1.96 m/s 2 until its engines stop at an altitude of 198.8 m. What is the maximum height reached by the rocket? Answer in units of m.

Answer 1

Answer:

Maximum height reached by the rocket, h = 202.62 meters            

Explanation:

It is given that,

Initial speed of the model rocket, u = 56.5 m/s

Constant upward acceleration, $a=1.96\ m/s^2$

Distance traveled by the engine until it stops, d = 198.8 m

Let v is the speed of the rocket when the engine stops. It can be calculated using the third equation of motion as :

$v=\sqrt{u^2+2ad}$

$v=\sqrt{(56.5)^2+2\times 1.96\times 198.8}$    

v = 63.02 m/s

At the maximum height, v = 0 and the engine now decelerate under the action of gravity, a = -g. Let h is the maximum height reached by the rocket.

Again using third equation of motion as :

$v^2-u^2=-2gh$

$h=\dfrac{v^2-u^2}{-2g}$

$h=\dfrac{u^2}{2g}$

$h=\dfrac{(63.02)^2}{2\times 9.8}$

h = 202.62 meters

So, the maximum height reached by the rocket is 202.62 meters. Hence, this is the required solution.