A pitcher throws a fastball with a velocity of 43.5 m/s. It is determined that during the windup and delivery the ball covers a displacement of 2.5 meters. This is from the point behind the body when the ball is at rest to the point of release. Calculate the acceleration during his throwing motion.
The correct answer and explanation is :
To calculate the acceleration of the pitcher’s fastball during his throwing motion, we can use the following kinematic equation:
[
v^2 = u^2 + 2a d
]
Where:
- ( v ) is the final velocity of the ball (43.5 m/s),
- ( u ) is the initial velocity of the ball (0 m/s, as it starts from rest),
- ( a ) is the acceleration (which we need to find),
- ( d ) is the displacement (2.5 meters).
Step 1: Plug the known values into the kinematic equation
[
(43.5)^2 = (0)^2 + 2a(2.5)
]
Simplifying the equation:
[
1892.25 = 5a
]
Step 2: Solve for acceleration ( a )
Now, isolate ( a ) by dividing both sides of the equation by 5:
[
a = \frac{1892.25}{5}
]
[
a = 378.45 \, \text{m/s}^2
]
Answer:
The acceleration of the ball during the pitcher’s throwing motion is 378.45 m/s².
Explanation:
The pitcher generates an initial force on the ball, which accelerates it from rest to its final velocity of 43.5 m/s during the windup and delivery phase. The displacement of 2.5 meters corresponds to the distance over which this acceleration occurs.
In physics, the acceleration is the rate of change of velocity with respect to time. In this scenario, the ball starts at rest and is rapidly accelerated through a distance of 2.5 meters, which results in the ball’s final velocity of 43.5 m/s. Using the kinematic equation allows us to relate the known parameters (initial velocity, final velocity, and displacement) to the acceleration. This high acceleration value reflects the intense force exerted by the pitcher on the ball, which is necessary to achieve such a high velocity in a short distance. The ball’s acceleration is quite large because the time over which it accelerates is very short, highlighting the rapid speed and power involved in a fast pitch.