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.
V = Vo + g*Tr = 0.
Tr = -Vo/g = -7.5/-9.81 = 0.77 s. = Rise
time.
Tf = Tr = 0.77 s. = Fall time.
V = Vo + g*Tf.
Vo = 0.
g = 9.81.
V = ?.
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To find the velocity of the ball when it returns to its starting point, we need to consider the following:
1. The initial velocity of the ball is +7.5 m/s.
2. The acceleration of gravity is -9.81 m/s^2 (downward direction).
When the ball reaches its maximum height, its velocity becomes zero. At this point, it starts falling back down, and its velocity increases in the downward direction due to gravity.
To find the velocity when the ball returns to its starting point, we can use the equation:
Final velocity = Initial velocity + (acceleration * time)
Since the ball returns to its starting point, we know the time it takes to reach the maximum height, and we can double it to find the total time of the ball's journey. Let's calculate it step by step:
Step 1: Calculate the time to reach the maximum height.
Using the equation:
Final velocity = Initial velocity + (acceleration * time)
0 m/s = 7.5 m/s + (-9.81 m/s^2 * t)
Rearranging the equation:
9.81 m/s^2 * t = 7.5 m/s
t = 7.5 m/s / 9.81 m/s^2
t ≈ 0.764 seconds
Step 2: Calculate the total time of the ball's journey.
Since the ball returns to its starting point, the total time of the ball's journey will be double the time to reach the maximum height.
Total time = 2 * 0.764 seconds
Total time ≈ 1.528 seconds
Step 3: Calculate the final velocity when the ball returns to its starting point.
Using the equation:
Final velocity = Initial velocity + (acceleration * time)
Final velocity = 7.5 m/s + (-9.81 m/s^2 * 1.528 seconds)
Final velocity ≈ -7.5 m/s
Therefore, the ball's velocity when it returns to its starting point will be approximately -7.5 m/s.
To find the velocity of the tennis ball when it returns to its starting point, we need to understand the motion of the ball and use the principles of kinematics.
When the ball is thrown vertically upward, its initial velocity is +7.5 m/s. Since the ball is thrown upwards, we can assume that its final velocity when it returns to the starting point will be negative. Let's call it Vf.
The acceleration of gravity, represented by "g," is acting downward and has a value of 9.81 m/s^2.
Using the equations of motion, we can relate the initial velocity, final velocity, acceleration, and displacement.
The equation we will use is: Vf^2 = Vi^2 + 2ad
Where:
- Vf is the final velocity
- Vi is the initial velocity
- a is the acceleration
- d is the displacement
In this case, the displacement is zero since the ball returns to its starting point. Therefore, we can simplify the equation to:
Vf^2 = Vi^2
Substituting the given values:
Vf^2 = (+7.5 m/s)^2
Calculating:
Vf^2 = 56.25 m^2/s^2
Taking the square root of both sides to solve for Vf:
Vf = ±7.5 m/s
Since we established that the final velocity when the ball returns will be negative, the velocity will be -7.5 m/s.
Therefore, the ball's velocity when it returns to its starting point is -7.5 m/s.