At the platform diving in the Olympics, a diver jumps from either a 5 meter, 7.5 meter or 10 meter board. Neglecting air resistance, calculate the diver's speed when she hits the water after diving off the 10 m board.
KE at end=PE at start
1/2 m vf^2=m g h
vf=sqrt (2gh) g=9.8m/s^2 h=10 m
To calculate the diver's speed when she hits the water after diving off the 10-meter board, we can use the principles of physics. Specifically, we can apply the equation of motion known as the kinematic equation.
The equation for calculating speed based on distance and acceleration is:
v^2 = u^2 + 2as
Where:
- v is the final velocity (speed) of the diver when she hits the water
- u is the initial velocity (which is 0 in this case)
- a is the acceleration due to gravity, approximately 9.8 m/s^2
- s is the distance covered by the diver when she jumps off the 10-meter board, which is 10 meters in this case.
Since the diver is starting from rest (u = 0), the equation simplifies to:
v^2 = 2as
Plugging in the values:
v^2 = 2 * 9.8 m/s^2 * 10 m
v^2 = 196 m^2/s^2
Therefore, the square of the final velocity (v^2) is equal to 196 m^2/s^2. To find the final velocity, we take the square root of this result:
v = √(196 m^2/s^2)
v ≈ 14 m/s
Hence, the diver's speed when she hits the water after diving off the 10-meter board is approximately 14 m/s.