A 51.8 kg pole vaulter running at 11.5 m/s vaults over the bar. Her speed when she is over the bar is 1.26 m/s. Neglect air resistance, as well as any energy absorbed by the pole, and determine her altitude as she crosses the bar
To determine the vaulter's altitude as she crosses the bar, we can use the principles of conservation of energy.
First, let's calculate the initial kinetic energy and the final kinetic energy of the vaulter.
The initial kinetic energy can be calculated using the equation:
KE_initial = (1/2) * mass * velocity^2
Plugging in the values, we get:
KE_initial = (1/2) * 51.8 kg * (11.5 m/s)^2
Next, we can calculate the final kinetic energy using the equation:
KE_final = (1/2) * mass * velocity^2
Plugging in the values, we get:
KE_final = (1/2) * 51.8 kg * (1.26 m/s)^2
According to the principle of conservation of energy, the initial kinetic energy should be equal to the final kinetic energy:
KE_initial = KE_final
(1/2) * 51.8 kg * (11.5 m/s)^2 = (1/2) * 51.8 kg * (1.26 m/s)^2
Now, we can solve this equation to find the velocity when the vaulter is over the bar.
(11.5 m/s)^2 = (1.26 m/s)^2
Solving for velocity, we get:
11.5 m/s = 1.26 m/s
Since the velocity is the same at both points, the vaulter's altitude when crossing the bar is equal to her initial altitude.