Question

to answer this question, first click here to view the associated video. a stone is projected at a 45° above the horizontal. at the peak of its trajectory, what types of energy does it possess? kinetic gravitational potential thermal energy due to its mass ($e = mc^{2}$) all of the above if the chemical energy stored in a 250 - calorie (1.0×10^{6} j) energy bar were converted into the kinetic energy of a 2200 - kg car, what would be the speed of the car (assuming it started from rest)? 30.2 m/s 21.3 m/s 909 m/s 60.4 m/s

Explanation:

Step1: Recall energy at peak of trajectory

At the peak of the trajectory of a projectile, the vertical - component of velocity is zero, but the horizontal - component of velocity is non - zero. So, it has kinetic energy due to its horizontal motion. Also, it is at a height above the ground, so it has gravitational potential energy. There is no information suggesting a change in temperature for thermal energy and the energy due to mass ($E = mc^{2}$) is not relevant in this context of classical mechanics.

Step2: Use kinetic energy formula for car problem

The kinetic energy formula is $K=\frac{1}{2}mv^{2}$. We know that the chemical energy of the energy bar is converted into kinetic energy of the car, so $K = 1.0\times10^{6}\text{ J}$ and $m = 2200\text{ kg}$. We need to solve for $v$ from the formula $v=\sqrt{\frac{2K}{m}}$.
Substitute $K = 1.0\times10^{6}\text{ J}$ and $m = 2200\text{ kg}$ into the formula:

$$v=\sqrt{\frac{2\times1.0\times 10^{6}}{2200}}$$

$$v=\sqrt{\frac{2\times10^{6}}{2200}}\approx\sqrt{909.09}\approx30.2\text{ m/s}$$

Answer:

1. Kinetic, Gravitational potential
2. 30.2 m/s