39. In a foot race, a runner maintains a kinetic energy of 931 Joules. What is the velocity of the runner if her mass is 57 kg ?

Question

UpStudy AI · Accepted Answer

To find the velocity of the runner, we can use the formula for kinetic energy:

$$ \text{Kinetic Energy} = \frac{1}{2} \times \text{Mass} \times \text{Velocity}^2 $$

Given:
- Kinetic Energy = 931 Joules
- Mass = 57 kg

We can rearrange the formula to solve for velocity:

$$ \text{Velocity} = \sqrt{\frac{2 \times \text{Kinetic Energy}}{\text{Mass}}} $$

Substitute the given values into the formula:

$$ \text{Velocity} = \sqrt{\frac{2 \times 931}{57}} $$

Now, we can calculate the velocity of the runner.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{\frac{2\times 931}{57}}$$
- step1: Reduce the fraction:
  $$\sqrt{\frac{98}{3}}$$
- step2: Use the properties of radicals:
  $$\frac{\sqrt{98}}{\sqrt{3}}$$
- step3: Simplify the expression:
  $$\frac{7\sqrt{2}}{\sqrt{3}}$$
- step4: Multiply by the Conjugate:
  $$\frac{7\sqrt{2}\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}$$
- step5: Multiply the numbers:
  $$\frac{7\sqrt{6}}{\sqrt{3}\times \sqrt{3}}$$
- step6: Multiply the numbers:
  $$\frac{7\sqrt{6}}{3}$$
The velocity of the runner is approximately 5.715476 m/s.
The runner's velocity is approximately 5.72 m/s.

39. In a foot race, a runner maintains a kinetic energy of 931 Joules. What is the velocity of the runner if her mass is 57 kg ?

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Physics Questions