A student drops the same 10 kilogram bowling ball three separate times. She drops the ball from heights of 1 meter, 2 meters, and 3 meters. Which graph correctly shows the ball’s kinetic energy when dropped from each height?
kinetic energy:
1. 20
2. 100
3. 200
4. 300
height (m):
1,2 or 3
To solve this problem, we need to understand that kinetic energy is given by the equation KE = 1/2mv^2, where m is the mass of the object (in this case, the bowling ball) and v is its velocity.
Since the mass of the bowling ball is the same (10 kilograms) for all three drops, the only factor that will affect its kinetic energy is the velocity at which it hits the ground.
To calculate the velocity at which the ball hits the ground, we can use the equation v = sqrt(2gh), where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height at which the ball is dropped.
For the first drop (h = 1 meter), the velocity will be v = sqrt(2 * 9.8 * 1) = sqrt(19.6) ≈ 4.43 m/s.
Using this velocity in the kinetic energy equation: KE = 1/2 * 10 * (4.43^2) = 97.81 ≈ 98 J.
For the second drop (h = 2 meters), the velocity will be v = sqrt(2 * 9.8 * 2) = sqrt(39.2) ≈ 6.26 m/s.
Kinetic energy: KE = 1/2 * 10 * (6.26^2) = 196.55 ≈ 197 J.
For the third drop (h = 3 meters), the velocity will be v = sqrt(2 * 9.8 * 3) = sqrt(58.8) ≈ 7.68 m/s.
Kinetic energy: KE = 1/2 * 10 * (7.68^2) = 295.94 ≈ 296 J.
Therefore, the correct graph should show the kinetic energy as:
1st drop (1 meter) ≈ 98 J
2nd drop (2 meters) ≈ 197 J
3rd drop (3 meters) ≈ 296 J
Since none of the given options matches these values, it seems that the correct graph is not available among the provided choices.