a tennis ball of mass 20g is released from rest at a height of 4m above the ground. on hitting the ground,it raises to a height of 3m.find the velocity with which it hits the ground.
falls 4 meters
v = -g t
h = Hi - (1/2) g t^2
g = 9.81 m/s^2
so
0 = 4 - 4.9 t^2
t^2 = 4/4.9
t = .904 seconds
v = -9.81 * .904 = -8.87 meters/second
To find the velocity with which the tennis ball hits the ground, we can use the law of conservation of energy. According to this principle, the total mechanical energy of the ball is conserved throughout its motion.
The mechanical energy of the ball consists of its kinetic energy (KE) and potential energy (PE). At the initial position, when the ball is at a height of 4m above the ground and at rest, all of its energy is potential energy. At the final position, when the ball reaches a height of 3m above the ground, the entire mechanical energy is converted to potential energy.
We can write the expression for the initial potential energy (PE_i) as:
PE_i = m * g * h_i
where m is the mass of the ball (20g = 0.02kg), g is the acceleration due to gravity (9.8 m/s^2), and h_i is the initial height (4m). Substituting the values, we have:
PE_i = 0.02kg * 9.8 m/s^2 * 4m
PE_i = 0.784 Joules
The expression for the final potential energy (PE_f) is:
PE_f = m * g * h_f
where h_f is the final height (3m). Substituting the values, we have:
PE_f = 0.02kg * 9.8 m/s^2 * 3m
PE_f = 0.588 Joules
According to the conservation of energy, the initial potential energy is equal to the final potential energy, and the difference between these two energies is the kinetic energy at the final position:
KE_f = PE_i - PE_f
KE_f = 0.784 Joules - 0.588 Joules
KE_f = 0.196 Joules
The kinetic energy (KE) is given by the equation:
KE = (1/2) * m * v^2
where v is the velocity of the ball. Substituting the known values, we can solve for v:
0.196 Joules = (1/2) * 0.02kg * v^2
0.196 Joules = 0.01kg * v^2
v^2 = 0.196 Joules / 0.01kg
v^2 = 19.6 m^2/s^2
v = sqrt(19.6 m^2/s^2)
v ≈ 4.43 m/s
Therefore, the velocity with which the tennis ball hits the ground is approximately 4.43 m/s.