Question

part 2 — questions: after completing the reading, answer the following questions. any data, calculations, or models you use to support your thinking should be explained. 1. which situation describes a system with decreasing gravitational potential energy? a. a girl stretching a horizontal spring b. a bicyclist riding up a steep hill c. a rocket rising vertically from earth d. a boy jumping down from a tree limb 2. what is the gravitational potential energy with respect to the surface of the water of a 75.0 - kilogram diver located 3.00 meters above the water? a. $2.17×10^{4}j$ b. $2.21×10^{3}j$ c. $2.25×10^{5}j$ d. $2.29×10^{3}j$

Explanation:

Question 1

Gravitational potential energy (GPE) is given by \( GPE = mgh \), where \( m \) is mass, \( g \) is acceleration due to gravity, and \( h \) is height. For GPE to decrease, height \( h \) should decrease (since \( m \) and \( g \) are constant for a system near Earth).

• Option a: Stretching a spring involves elastic potential energy, not gravitational.
• Option b: Riding up a hill increases height, so GPE increases.
• Option c: Rocket rising increases height, GPE increases.
• Option d: Boy jumping down decreases height (from tree limb to lower position), so GPE decreases.

Step 1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy is \( GPE = mgh \), where \( m = 75.0 \, \text{kg} \), \( g = 9.8 \, \text{m/s}^2 \), and \( h = 3.00 \, \text{m} \).

Step 2: Substitute the values into the formula

\[
GPE = 75.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3.00 \, \text{m}
\]

Step 3: Calculate the product

First, multiply \( 75.0 \times 9.8 = 735 \). Then, multiply \( 735 \times 3.00 = 2205 \, \text{J} \), which is approximately \( 2.21 \times 10^3 \, \text{J} \).

Answer:

d. a boy jumping down from a tree limb

Question 2