65 kg pole vaulter running at 10.2 m/s vaults over the bar. if height of bar was set at 4.96 m how fast was he moving as he cleared the bar
If he cleared the bar at the top of his swing, then all his speed was horizontal, at 10.2 m/s.
All that stuff about mass and height is just noise. Trying to incorporate other forces is impossible without further data.
To determine how fast the pole vaulter was moving as he cleared the bar, we can use the law of conservation of energy. The total mechanical energy of the pole vaulter can be equated before and after the vault, considering both kinetic energy (due to his velocity) and potential energy (due to his height above the ground).
Before the vault, the total mechanical energy is given by:
Initial Energy = (1/2) × mass × velocity^2
After the vault, the total mechanical energy is given by:
Final Energy = mass × gravitational acceleration × height
We can set these two equations equal to each other and solve for the velocity:
(1/2) × mass × velocity^2 = mass × gravitational acceleration × height
Simplifying the equation, we get:
velocity^2 = 2 × gravitational acceleration × height
Plugging in the known values:
mass = 65 kg
height = 4.96 m
gravitational acceleration (standard value) = 9.8 m/s^2
velocity^2 = 2 × 9.8 m/s^2 × 4.96 m
velocity^2 = 96.512 m^2/s^2
Taking the square root of both sides to solve for velocity, we get:
velocity = square root of (96.512 m^2/s^2)
velocity ≈ 9.825 m/s
Therefore, the pole vaulter was moving at approximately 9.825 m/s as he cleared the bar.