To determine the velocity of the ball after it turns back, we need to consider the conservation of energy. When the ball is thrown at the building, it possesses kinetic energy due to its initial velocity. This kinetic energy is then converted into potential energy as the ball reaches its highest point, and finally, it converts back into kinetic energy as it returns to the ground.
The law of conservation of mechanical energy states that the total mechanical energy of a system remains constant as long as no external forces (such as friction or air resistance) are acting on it. In this case, we can assume that there is no significant energy loss due to external factors.
The initial kinetic energy of the ball can be calculated using the formula:
KE_initial = (1/2) * m * v_initial^2
Where: m = mass of the ball = 1 kg v_initial = initial velocity of the ball = 8 m/s
Substituting the given values into the formula:
KE_initial = (1/2) * 1 kg * (8 m/s)^2 = 32 J
Since the total mechanical energy is conserved, the final kinetic energy of the ball when it turns back will also be 32 J. We can calculate the final velocity of the ball using the formula for kinetic energy:
KE_final = (1/2) * m * v_final^2
Substituting the known values:
32 J = (1/2) * 1 kg * (v_final)^2
Simplifying the equation:
(v_final)^2 = 64 v_final = √64 v_final = 8 m/s
Therefore, the velocity of the ball when it turns back is 8 m/s.