A baseball has a velocity of 44.0 m/s,
directed horizontally, as it is released
by a pitcher. The ball’s velocity 0.0100
s before it is released is 42.0 m/s,
directed 3.00 degrees above the
horizontal. Estimate the ball’s
instantaneous acceleration just
before it is released.
To estimate the ball's instantaneous acceleration just before it is released, we can use the definition of acceleration as the rate of change of velocity.
First, let's break down the information given in the problem:
Initial velocity (0.0100 s before release):
Magnitude: 42.0 m/s
Direction: 3.00 degrees above the horizontal
Final velocity (at the moment of release):
Magnitude: 44.0 m/s
Direction: horizontally
To find the instantaneous acceleration, we need to determine the change in velocity and divide it by the time taken:
1. Find the change in velocity: Subtract the initial velocity from the final velocity.
Magnitude: 44.0 m/s - 42.0 m/s = 2.0 m/s
Direction: The final velocity is horizontal, so the change in direction is 0 degrees.
2. Calculate the time taken: Since the problem mentions the velocities at 0.0100 s before release and at release, we can assume that the time taken is 0.0100 seconds.
3. Calculate the instantaneous acceleration: Divide the change in velocity by the time taken.
Magnitude: 2.0 m/s / 0.0100 s = 200 m/s²
Direction: Since the final velocity is horizontal and the change in direction is 0 degrees, the acceleration is also horizontal.
Therefore, the estimated instantaneous acceleration of the ball just before it is released is approximately 200 m/s² horizontally.
To estimate the ball's instantaneous acceleration just before it is released, we can use the following formula:
instantaneous acceleration = (final velocity - initial velocity) / time
Given:
- Initial velocity (0.0100 s before release): 42.0 m/s at 3.00 degrees above the horizontal.
- Final velocity (at release): 44.0 m/s horizontally.
- Time: 0.0100 s
First, let's break down the initial velocity into its horizontal and vertical components:
Initial velocity (horizontal component) = initial velocity cosθ
= 42.0 m/s * cos(3.00°)
Initial velocity (vertical component) = initial velocity sinθ
= 42.0 m/s * sin(3.00°)
Since the ball is released horizontally, the initial velocity's vertical component doesn't affect the instantaneous acceleration.
Now, let's calculate the acceleration using the given information:
instantaneous acceleration = (final velocity - initial velocity) / time
Since the final velocity is purely horizontal, we can calculate the acceleration only in the horizontal direction:
instantaneous acceleration = (44.0 m/s - (42.0 m/s * cos(3.00°))) / 0.0100 s
Calculating this expression will give you the estimate of the ball's instantaneous acceleration just before it is released.