Respuesta :
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, [tex]a=1.96\ m/s^2[/tex]
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 :
[tex]v=\sqrt{u^2+2ad}[/tex]
[tex]v=\sqrt{(56.5)^2+2\times 1.96\times 198.8}[/tex]
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 :
[tex]v^2-u^2=-2gh[/tex]
[tex]h=\dfrac{v^2-u^2}{-2g}[/tex]
[tex]h=\dfrac{u^2}{2g}[/tex]
[tex]h=\dfrac{(63.02)^2}{2\times 9.8}[/tex]
h = 202.62 meters
So, the maximum height reached by the rocket is 202.62 meters. Hence, this is the required solution.
