Question

a group of skydivers gains speed as they fall together. a graph relating the groups kinetic energy in kilojoules (kj) and their speed in meters per second (\\(\frac{m}{s}\\)) is shown below. use the pattern on the graph to complete the prediction. - when the groups speed is 40 \\(\frac{m}{s}\\), their kinetic energy will be \\(\square\\) kj.

Explanation:

Step1: Identify the relationship

Kinetic energy \( KE \) and speed \( v \) relationship from the graph: when \( v = 20 \, \text{m/s} \), \( KE = 80 \, \text{kJ} \). Notice that kinetic energy is proportional to the square of speed (since \( KE=\frac{1}{2}mv^2 \), and the graph is a parabola, indicating \( KE \propto v^2 \)).

Step2: Set up the proportion

Let \( KE_1 = 80 \, \text{kJ} \), \( v_1 = 20 \, \text{m/s} \), \( v_2 = 40 \, \text{m/s} \), \( KE_2 = ? \)

Since \( KE \propto v^2 \), we have \( \frac{KE_1}{v_1^2} = \frac{KE_2}{v_2^2} \)

Substitute values: \( \frac{80}{20^2} = \frac{KE_2}{40^2} \)

Step3: Solve for \( KE_2 \)

First, calculate \( 20^2 = 400 \), \( 40^2 = 1600 \)

So, \( \frac{80}{400} = \frac{KE_2}{1600} \)

Cross - multiply: \( 400 \times KE_2 = 80\times1600 \)

\( 400\times KE_2 = 128000 \)

Divide both sides by 400: \( KE_2=\frac{128000}{400}=320 \)

Answer:

320