A tennis ball is thrown vertically upward with
an initial velocity of +7.5 m/s.
What will the ball’s velocity be when it
returns to its starting point? The acceleration
of gravity is 9.81 m/s
2
.
Answer in units of m/s
How long will the ball take to reach its starting
point?
Answer in units of s
To find the velocity of the tennis ball when it returns to its starting point, we can use the equation:
Final velocity (v) = Initial velocity (u) + Acceleration (a) * Time (t)
Since the tennis ball is thrown vertically upward, the acceleration is downward and equal to the acceleration due to gravity, which is -9.81 m/s^2 (negative because it is acting in the opposite direction to the initial velocity).
Given:
Initial velocity (u) = +7.5 m/s
Acceleration (a) = -9.81 m/s^2
We need to find the time taken for the ball to reach its starting point, which is the time it takes for the velocity to become zero.
Using the same equation, but with the final velocity (v) equal to zero, we can solve for time (t).
0 = +7.5 - 9.81 * t
Rearranging the equation, we have:
9.81 * t = 7.5
t = 7.5 / 9.81
Solving this, we find:
t ≈ 0.764 seconds
Therefore, it takes approximately 0.764 seconds for the ball to reach its starting point.
Now, let's find the velocity of the ball when it returns to its starting point.
Using the same equation and plugging in the values:
Final velocity (v) = +7.5 - 9.81 * 0.764
v ≈ 7.5 - 7.49
v ≈ 0.01 m/s
Therefore, the ball's velocity when it returns to its starting point is approximately 0.01 m/s.
To find the velocity when the ball returns to its starting point, we can use the equation for the final velocity of an object under constant acceleration:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Given:
Initial velocity (u) = +7.5 m/s (upward direction)
Acceleration (a) = -9.81 m/s^2 (acceleration due to gravity)
Since the ball is thrown upwards, the acceleration due to gravity is acting in the opposite direction as the initial velocity. Therefore, we take the acceleration as negative.
To find the time it takes for the ball to reach its starting point, we can use the equation for displacement:
v^2 = u^2 + 2as
where u is the initial velocity, v is the final velocity, a is the acceleration, and s is the displacement.
In this case, the displacement (s) is zero because the ball returns to its starting point. So, the equation becomes:
v^2 = u^2 + 2as
v^2 = (7.5)^2 + 2(-9.81)(0)
v^2 = 56.25
Taking the square root of both sides, we get:
v = sqrt(56.25) = 7.5 m/s
Therefore, the velocity of the ball when it returns to its starting point is 7.5 m/s.
Now, to find the time it takes for the ball to reach its starting point, since the displacement is zero, we can use the equation:
v = u + at
Since we are solving for time (t), we rearrange the equation as:
t = (v - u) / a
Substituting the given values:
t = (0 - 7.5) / -9.81
t = -7.5 / -9.81
t ≈ 0.764 s
Therefore, the ball will take approximately 0.764 seconds to reach its starting point.
Vfinal = Vinitial
(Consider conservation of energy)
Time (up and down)
= 2*Vinitial/g
= 2*7.5/9.8 = ___ s