Calculating Time of Flight, Range, and Final Velocity of a Tennis Ball
a) What will the time of flight be for a tennis ball launched by the ball machine? (3)
b) What will the range of the tennis ball be? (2)
c) What will be the final velocity of the ball with which it reaches the ground? (3)
Answer:
a) The time of flight for a tennis ball launched by the ball machine is 0.19 seconds.
b) The range of the tennis ball is 1.01 meters.
c) The final velocity of the ball when it reaches the ground is 7.16 m/s.
Time of Flight of Tennis Ball
The time of flight of the tennis ball is calculated using the formula h = vt + ¹/₂gt² where h is the height, v is the initial velocity, t is the time, and g is the acceleration due to gravity.
Plugging in the values, we get:
1.2 = 5.3t + 0.5(9.8)t²
After solving the quadratic equation, we find that t = 0.19 seconds. Therefore, the time of flight for the tennis ball is 0.19 seconds.
Range of the Tennis Ball
The range of the tennis ball is calculated using the formula R = vt, where R is the range, v is the initial velocity, and t is the time of flight.
Substituting the values, we get:
R = 5.3 x 0.19 = 1.01 meters. Hence, the range of the tennis ball is 1.01 meters.
Final Velocity of the Ball
The final velocity of the ball when it reaches the ground can be found using the formula vf = vo + gt, where vf is the final velocity, vo is the initial velocity, g is the acceleration due to gravity, and t is the time of flight.
Substituting the values, we get:
vf = 5.3 + 9.8(0.19) = 7.16 m/s. Therefore, the final velocity of the ball when it reaches the ground is 7.16 m/s.