Question

Jason launches a model rocket with a mass of 2.0 kg from his spring-powered rocket launcher with a spring constant of 800 N/m. He pulls it back .55 m. If Jason aims it straight up, what potential energy will the rocket have when it reaches its maximum height? What height will it reach?

Answer 1

121 Joules

6.16717 m

Step-by-step explanation:

m = Mass of the rocket = 2 kg

k = Spring constant = 800 N/m

x = Compression of spring = 0.55 m

Here, the kinetic energy of the spring and rocket will balance each other

`(1)/(2)mu^2=(1)/(2)kx^2\\\Rightarrow u=\sqrt{(kx^2)/(m)}\\\Rightarrow u=\sqrt{(800* 0.55^2)/(2)}\\\Rightarrow u=11\ m/s`

The initial velocity of the rocket is 11 m/s = u.

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.81 m/s² = g

`v^2-u^2=2as\\\Rightarrow s=(v^2-u^2)/(2a)\\\Rightarrow s=(0^2-11^2)/(2* -9.81)\\\Rightarrow s=6.16717\ m`

The maximum height of the rocket will be 6.16717 m

Potential energy is given by

`P=mgh\\\Rightarrow P=2* 9.81* (0^2-11^2)/(2* -9.81)\\\Rightarrow P=121\ J`

The potential energy of the rocket at the maximum height will be 121 Joules