At the 2014 ALCS game 2, the Royals started their right-handed pitcher Wade Davis whose fastball typically reaches 94 mph. if his throwing motion covers 2.8m from the position where his arm starts to make forward motion to release position, and the mass of the ball is 0.5lbs.
(a) find the acceleration of the ball?
(b)how long did it take him to throw the ball (from the position where his arm starts to make a forward motion to the release of the ball)?
(c) what is the force exerted on the ball?
To answer these questions, we need to use some physics formulas and equations related to motion and forces.
(a) To find the acceleration of the ball, we can use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
We are given that the initial velocity is 0 mph (since the ball starts from rest), and the final velocity is 94 mph. However, we need to convert these velocities to m/s before plugging them into the formula.
Converting mph to m/s:
1 mph = 0.447 m/s
So, initial velocity = 0 mph = 0 m/s
And, final velocity = 94 mph = 94 * 0.447 m/s = 42.168 m/s
Next, we need to find the time it takes for the ball to accelerate over the given distance. We can use the formula for distance:
distance = (initial velocity + final velocity) * time / 2
Plugging in the values:
distance = 2.8 m
initial velocity = 0 m/s
final velocity = 42.168 m/s
Rearranging the formula to solve for time:
time = (2 * distance) / (initial velocity + final velocity)
Now, let's calculate the acceleration.
acceleration = (final velocity - initial velocity) / time
acceleration = (42.168 m/s - 0 m/s) / time
We'll solve for time first.
time = (2 * 2.8 m) / (0 m/s + 42.168 m/s)
time = 5.6 m / 42.168 m/s
time = 0.133 sec
Now, plugging the time value back into the acceleration formula:
acceleration = (42.168 m/s - 0 m/s) / 0.133 sec
acceleration = 317.203 m/s^2
Therefore, the acceleration of the ball is approximately 317.203 m/s^2.
(b) To find how long it took to throw the ball, we have already calculated the time in part (a). The time is approximately 0.133 seconds.
(c) To find the force exerted on the ball, we can use Newton's second law of motion:
force = mass * acceleration
Given that the mass of the ball is 0.5 lbs, we need to convert it to kg:
1 lb = 0.4536 kg
mass = 0.5 lbs = 0.5 * 0.4536 kg = 0.2268 kg
Now, we can calculate the force:
force = 0.2268 kg * 317.203 m/s^2
force = 71.907 N
Therefore, the force exerted on the ball is approximately 71.907 Newtons.