A toy rocket that weighs 10 N blasts straight up from ground level with an initial kinetic energy of 40 J. At the exact top of its trajectory, its total mechanical energy is 140 J. To what vertical height
Above the ground does it rise, assuming no air resistance?
A) 14 m
B) 10 m
C) 24 m
D) 1.0 m

Question

Quizplus · Accepted Answer

The total mechanical energy at the top of the trajectory is given as 140 J, which is the sum of the kinetic energy (which is 0 J at the top, since the rocket is momentarily at rest) and the potential energy. The initial kinetic energy is 40 J, and since there's no air resistance, mechanical energy is conserved. Thus, the increase in potential energy (which equals the total mechanical energy at the top minus the initial kinetic energy) is 140 J - 40 J = 100 J. The potential energy is given by $PE = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$), and $h$ is the height. The weight of the rocket is given as 10 N, which is the force due to gravity, so $m = \frac{Weight}{g} = \frac{10 \, \text{N}}{9.8 \, \text{m/s}^2}$. Solving for $h$, we get $h = \frac{PE}{mg} = \frac{100 \, \text{J}}{10 \, \text{N}} = 10 \, \text{m}$.

A Toy Rocket That Weighs 10 N Blasts Straight Up