A boy is running with a kinetic energy of 810 J. If the boy has a mass of 80 kg, what is his speed?A.10.1 m/sB.3.2 m/sC.4.5 m/sD.6.2 m/s

1. Break Down the Problem

To find the speed of the boy given his kinetic energy and mass, we need to use the kinetic energy formula:

$KE = \frac{1}{2} mv^2$

Where:

• $KE$ is the kinetic energy,
• $m$ is the mass,
• $v$ is the speed.

We'll rearrange the formula to find speed $v$.

2. Relevant Concepts

The formula for kinetic energy is:

$KE = \frac{1}{2} mv^2$

Rearranging for $v$ gives us:

$v = \sqrt{\frac{2KE}{m}}$

3. Analysis and Detail

Substituting the known values into the rearranged formula:

• $KE = 810 \, \text{J}$
• $m = 80 \, \text{kg}$

We calculate $v$:

$v = \sqrt{\frac{2 \times 810 \, \text{J}}{80 \, \text{kg}}}$

Carrying out the calculation step-by-step:

1. Calculate $2 \times 810 = 1620$.
2. Divide by mass: $\frac{1620}{80} = 20.25$
3. Take the square root: $v = \sqrt{20.25} \approx 4.5 \, \text{m/s}$

4. Verify and Summarize

We can verify the calculation:

1. When $v \approx 4.5 \, \text{m/s}$: $KE = \frac{1}{2} \cdot 80 \cdot (4.5)^2 = 810 \, \text{J}$ This confirms our calculation is correct.

Final Answer

The speed of the boy is approximately 4.5 m/s, so the answer is C. 4.5 m/s.