Question
When a 65 kg skydiver jumps from a plane, her speed steadily increases until air resistance provides a force that balances the force due to free fall. How fast is the skydiver falling if her kinetic energy at the moment is 7.04 x 10^5 J?
Answers
GPT-4o mini
To determine the speed of the skydiver, we can use the formula for kinetic energy, which is given by:
\[
KE = \frac{1}{2} mv^2
\]
where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass of the skydiver,
- \( v \) is the velocity.
Given:
- \( KE = 7.04 \times 10^5 \, J \)
- \( m = 65 \, kg \)
We can rearrange the kinetic energy formula to solve for \( v \):
\[
v = \sqrt{\frac{2 \times KE}{m}}
\]
Substituting the values we have:
\[
v = \sqrt{\frac{2 \times 7.04 \times 10^5 \, J}{65 \, kg}}
\]
Calculating the numerator:
\[
2 \times 7.04 \times 10^5 \, J = 1.408 \times 10^6 \, J
\]
Now, calculate the whole expression:
\[
v = \sqrt{\frac{1.408 \times 10^6 \, J}{65 \, kg}} \approx \sqrt{21678.46 \, \text{m}^2/\text{s}^2}
\]
Finally, taking the square root:
\[
v \approx 147.12 \, \text{m/s}
\]
Thus, the speed of the skydiver is approximately \( 147.12 \, \text{m/s} \).
\[
KE = \frac{1}{2} mv^2
\]
where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass of the skydiver,
- \( v \) is the velocity.
Given:
- \( KE = 7.04 \times 10^5 \, J \)
- \( m = 65 \, kg \)
We can rearrange the kinetic energy formula to solve for \( v \):
\[
v = \sqrt{\frac{2 \times KE}{m}}
\]
Substituting the values we have:
\[
v = \sqrt{\frac{2 \times 7.04 \times 10^5 \, J}{65 \, kg}}
\]
Calculating the numerator:
\[
2 \times 7.04 \times 10^5 \, J = 1.408 \times 10^6 \, J
\]
Now, calculate the whole expression:
\[
v = \sqrt{\frac{1.408 \times 10^6 \, J}{65 \, kg}} \approx \sqrt{21678.46 \, \text{m}^2/\text{s}^2}
\]
Finally, taking the square root:
\[
v \approx 147.12 \, \text{m/s}
\]
Thus, the speed of the skydiver is approximately \( 147.12 \, \text{m/s} \).