A tennis player tosses a tennis ball straight up and then catches it after 1.76 s at the same height as the point of release.
(a) What is the acceleration of the ball while it is in flight?
magnitude:m/s2=
direction
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(b) What is the velocity of the ball when it reaches its maximum height?
magnitude:m/s=
direction
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(c) Find the initial velocity of the ball.
m/s upward
(d) Find the maximum height it reaches.
m
To find the answers to these questions, we can use the kinematic equations of motion. These equations relate the initial velocity, final velocity, acceleration, distance, and time of an object in motion.
(a) To find the acceleration of the ball while it is in flight, we can use the kinematic equation:
Vf = Vi + at
Where Vf is the final velocity, Vi is the initial velocity, a is the acceleration, and t is the time.
In this case, the ball is caught at the same height as its point of release, which means its final velocity at the top is 0 m/s. The initial velocity can be assumed to be the same magnitude but in the opposite direction (since the ball is thrown upwards). The time is given as 1.76 s.
Therefore, the equation becomes:
0 = Vi + a * 1.76
Solving for a, we get:
a = -Vi / 1.76
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity (i.e., downward).
(b) To find the velocity of the ball when it reaches its maximum height, we can use the kinematic equation:
Vf = Vi + at
In this case, since the ball reaches its maximum height, the final velocity is 0 m/s. The acceleration is the same as calculated in part (a) (-Vi / 1.76). We need to find Vi, the initial velocity.
Therefore, the equation becomes:
0 = Vi + (-Vi / 1.76) * t
Solving for Vi, we get:
Vi = Vi / 1.76
This means that the magnitude of the initial velocity is equal to its magnitude divided by 1.76.
(c) To find the initial velocity of the ball, we can use the equation derived in part (b). The magnitude of the initial velocity is equal to its magnitude divided by 1.76.
(d) To find the maximum height reached by the ball, we can use the kinematic equation:
h = Vi * t + (1/2) * a * t^2
In this case, Vi is the initial velocity calculated in part (c), t is the time given (1.76 s), and a is the acceleration calculated in part (a).
By substituting these values into the equation, we can find the maximum height attained by the ball.