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 \( 147.12 , \text{m/s} \).
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