Question

1. if rooney is cross - country skiing, has a mass of 56.7 kg, and her kinetic energy is 3674 j, what is her speed? 3.6 m/s 28.4 m/s 5.7 m/s 6.5 m/s

Explanation:

Step1: Recall kinetic - energy formula

The formula for kinetic energy is $KE=\frac{1}{2}mv^{2}$, where $KE$ is kinetic energy, $m$ is mass, and $v$ is speed. We need to solve for $v$.

Step2: Rearrange the formula for $v$

Starting from $KE = \frac{1}{2}mv^{2}$, we can first multiply both sides by 2 to get $2KE=mv^{2}$. Then divide both sides by $m$: $v^{2}=\frac{2KE}{m}$. Finally, take the square - root of both sides: $v=\sqrt{\frac{2KE}{m}}$.

Step3: Substitute the given values

We are given that $m = 56.7$ kg and $KE=367.4$ J. Substitute these values into the formula: $v=\sqrt{\frac{2\times367.4}{56.7}}$.
First, calculate the value inside the square - root: $\frac{2\times367.4}{56.7}=\frac{734.8}{56.7}\approx12.96$.
Then, find the square root: $v=\sqrt{12.96} = 3.6$ m/s.

Answer:

3.6 m/s