Answer:
10 m/s
Explanation:
The work-kinetic energy theorem states that the net work done on an object is equal to the change in the kinetic energy of the object.
In formula:
\(W=K_f -K_i\) (1)
where
W is the work done
Ki is the initial kinetic energy
Kf is the final kinetic energy
In this problem, we have:
\(W=-5000 J\) the net work done on the gymnast
\(m=100 kg\) is the mass of the gymnast
\(v_f = 0\) is the final velocity of the gymnast, so her final kinetic energy is also zero:
\(K_f = \frac{1}{2}mv_f^2 = 0\)
Therefore, we can rewrite eq.(1) as
\(W=-\frac{1}{2}mv_i^2\)
where \(v_i\) is the initial velocity of the girl. By substituting the numbers and re-arranging the equation, we find:
\(v_i = \sqrt{-\frac{2W}{m}}=\sqrt{-\frac{2(-5000 J)}{100 kg}}=10 m/s\)
