Answer :
Final answer:
The tennis ball takes approximately 2.04 seconds to reach its maximum height. The velocity of the ball 3.0 seconds after it is thrown is approximately 9.4 m/s, downward.
Explanation:
To determine the time it takes for the tennis ball to reach its maximum height, we can use the equation:
t = v / g
where t is the time, v is the initial vertical velocity, and g is the acceleration due to gravity. In this case, the initial vertical velocity is 20.0 m/s, and the acceleration due to gravity is 9.8 m/s². Therefore, the time it takes for the tennis ball to reach its maximum height is approximately 2.04 seconds.
To determine the velocity of the ball 3.0 seconds after it is thrown, we can use the equation:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Since the ball is shot vertically upward, the acceleration due to gravity is -9.8 m/s². Therefore, the velocity of the ball 3.0 seconds after it is thrown is approximately 9.4 m/s, downward.
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The ball's height at time t is
y = (20.0 m/s) t - 1/2 g t²
where g is the acceleration due to gravity, with magnitude 9.80 m/s².
Also, recall that
v² - u² = 2 a ∆y
where u is the initial velocity, v is the final velocity, a is the acceleration, and ∆y is the change in height. Let Y be the maximum height. At this height, v = 0, so
- (20.0 m/s)² = 2 (-g) Y
==> Y ≈ 20.408 m
Plug this into the first equation and solve for t :
Y = (20.0 m/s) t - 1/2 (9.80 m/s²) t²
==> t ≈ 2.04 s
The ball's velocity at time t is
v = 20.0 m/s - g t
After t = 3.0 s, its velocity will be
v = 20.0 m/s - (9.80 m/s²) (3.0 s)
v = -9.40 m/s
or 9.40 m/s in the downward direction.
