Initially, a baseball was held by one pitcher.
The fastest measured pitched baseball left the pitcher’s hand at a speed of 45m/s. If the pitcher was in contact with the ball over a
distance of 1.5m and produced constant acceleration,
a)What acceleration did he give the ball?
b)How much time did it take him to pitch it?
Solve these:
v = at
s = 1/2 at^2
speed 0 to 45 m/s over 1.5 meters at constant a
how long was it in his hand?
v = a t, so v linear in time
so average speed = 45/2 =22.5 m/s
so time in hand= 1.5 /22.5 = 0.0667 seconds (ans part b)
v = a t still
45 = a (0.0667)
a = 675 m /s^2
by the way, 45m/s is 100 miles per hour. Really?
To find the acceleration (a), we can use the following formula:
v^2 = u^2 + 2as
where:
v = final velocity = 45 m/s
u = initial velocity = 0 m/s (since the ball was initially at rest)
s = distance = 1.5 m
Given that the pitcher produces constant acceleration, we can assume that the initial velocity is 0 m/s. Now we can plug in the values into the formula and solve for a:
45^2 = 0^2 + 2a(1.5)
2025 = 3a
a = 2025 / 3
a = 675 m/s^2
So, the acceleration given by the pitcher is 675 m/s^2.
To find the time (t) it took to pitch the ball, we can use the following formula:
v = u + at
We can rearrange this equation to solve for t:
t = (v - u) / a
Substituting the given values, we get:
t = (45 - 0) / 675
t = 0.067 seconds
Therefore, it took him approximately 0.067 seconds to pitch the ball.
To find the acceleration given to the ball by the pitcher, you can use the following equation:
v^2 = u^2 + 2as
Where:
v = final velocity (45 m/s)
u = initial velocity (0 m/s, as the ball is initially at rest)
s = distance covered (1.5 m)
a = acceleration (unknown)
Now, let's rearrange the equation to solve for acceleration:
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (45^2 - 0^2) / (2 * 1.5)
Simplifying the equation:
a = 2025 / 3
a ≈ 675 m/s^2
So, the acceleration given by the pitcher to the ball is approximately 675 m/s^2.
To find the time it took the pitcher to pitch the ball, you can use the following equation:
v = u + at
Where:
v = final velocity (45 m/s)
u = initial velocity (0 m/s, as the ball is initially at rest)
a = acceleration (675 m/s^2)
t = time (unknown)
Rearranging the equation to solve for time:
t = (v - u) / a
Substituting the given values:
t = (45 - 0) / 675
Simplifying the equation:
t = 0.0667 seconds
So, it took approximately 0.0667 seconds for the pitcher to pitch the ball.