13)
Recall, the law of conservation of energy states that energy is not created nor destroyed but it is converted from one form to another. At the initial positions of the balls above the ground, each has potential energy. As they begin to fall, the potential energy is converted to kinetic energy. As they reach the floor, the energy is fully kinetic
Thus,
potential energy of ball at the top = kinetic energy at the bottom
The formula for calculating potential energy, PE is expressed as
PE = mgh
where
m is the mass of the ball
h is the height above the ground
g is the acceleration due to gravity
The formula for calculating kinetic energy, KE is expressed as
KE = 1/2mv^2
where
m is the mass of the ball
v is the velocity of the ball
Considering the basketball,
m = 0.58
h = 2
g = 10m/s^2
mgh = 1/2mv^2
By substituting these values into the equation, we have
0.58 x 10 x 2 = 1/2 x 0.58 x v^2
11.6 = 0.29v^2
Dividing both sides of the equation by 0.29, we have
11/6/0.29 = 0.29v^2/0.29
v^2 = 40
v = square root of 40
v = 6.32 m/s
The speed of the basketball on hitting the ground is 6.32 m/s
The kinetic energy = 1/2 x 0.58 x 40 = 11.6 J
For the Tennis ball,
m = 0.058
h = 2
0.058 x 10 x 2 = 1/2 x 0.058 x v^2
0.029v^2 = 20
v^2 = 20/0.029 =