Question

7.) an archer stands on the ground and fires an arrow at a target. a second archer stands at the top of a building and holds an arrow in his hand. which arrow has more potential energy? explain. 8.) in the same scenario described in question 7, which arrow has more kinetic energy? explain.

Explanation:

For Question 7 (Potential Energy Comparison)

Step1: Recall Potential Energy Formula

The formula for gravitational potential energy is $PE = mgh$, where $m$ is mass, $g$ is acceleration due to gravity, and $h$ is height above a reference point (here, ground level).

Step2: Analyze the Archers' Heights

The first archer is on the ground ($h_1 = 0$ relative to ground), so his arrow's $PE_1 = mg(0) = 0$. The second archer is at the top of a building, so his arrow has a height $h_2 > 0$. Assuming both arrows have the same mass ($m$) and $g$ is constant, $PE_2 = mgh_2 > 0$.

Step3: Compare Potential Energies

Since $PE_1 = 0$ and $PE_2 > 0$, the arrow held by the archer at the top of the building has more potential energy.

Step1: Recall Kinetic Energy Formula

Kinetic energy is given by $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity.

Step2: Analyze Arrow Motions

The first archer fires the arrow, so its velocity $v_1 > 0$ (it is moving). The second archer holds the arrow, so its velocity $v_2 = 0$ (stationary). Assume both arrows have the same mass ($m$).

Step3: Compare Kinetic Energies

For the fired arrow: $KE_1 = \frac{1}{2}m(v_1)^2 > 0$ (since $v_1 > 0$). For the held arrow: $KE_2 = \frac{1}{2}m(0)^2 = 0$. Thus, $KE_1 > KE_2$.

Answer:

The arrow held by the archer at the top of the building has more potential energy. This is because gravitational potential energy ($PE = mgh$) depends on height ($h$) above the ground; the second archer’s arrow is at a greater height ($h > 0$) than the first archer’s arrow (at $h = 0$), so with the same mass and gravity, it has more potential energy.

For Question 8 (Kinetic Energy Comparison)