What is the minimum speed you would need to roll a lacrosse ball down a flat street for it to be able to roll over a speed bump with a height of 12 cm

To determine the minimum speed needed to roll a lacrosse ball over a speed bump, we can use the principle of conservation of energy. The ball needs enough initial kinetic energy to overcome the potential energy barrier represented by the height of the speed bump.

To calculate the minimum speed, we can equate the initial kinetic energy to the potential energy difference between the starting point and the top of the speed bump. The kinetic energy equation is given as:

KE = (1/2)mv²

where KE represents the kinetic energy, m is the mass of the ball, and v is the speed. The potential energy equation is given as:

PE = mgh

where PE represents potential energy, m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the speed bump (12 cm or 0.12 m).

Setting the initial kinetic energy equal to the potential energy difference:

(1/2)mv² = mgh

Canceling out the m (mass) from both sides:

(1/2)v² = gh

Solving for v:

v² = 2gh

v = √(2gh)

Now, substituting g = 9.8 m/s² and h = 0.12 m into the equation:

v = √(2 * 9.8 * 0.12)

v ≈ √(2 * 1.176)

v ≈ √(2.352)

v ≈ 1.53 m/s

Therefore, to roll a lacrosse ball over a speed bump with a height of 12 cm, you would need a minimum speed of approximately 1.53 meters per second or 5.03 feet per second.