if a pitcher throws a ball at 101 mph and it trvels 60.5 feet. How much wiil it drop?
To determine how much the ball will drop, we need to consider the effect of gravity on the ball's trajectory. The formula to calculate the vertical drop is given by the equation:
d = 1/2 * g * (t^2)
where:
- d is the vertical distance or drop
- g is the acceleration due to gravity (approximately 32.2 ft/s^2)
- t is the time it takes for the ball to travel the given distance
To find the time (t), we can use the formula:
t = distance / velocity
Given that the velocity is 101 mph (miles per hour) and the distance is 60.5 feet, we need to convert the velocity to feet per second before calculating the time. 1 mph is equal to 1.47 ft/s.
Converting the velocity:
101 mph * 1.47 ft/s = 148.47 ft/s
Now we can calculate the time:
t = 60.5 ft / 148.47 ft/s = 0.408 seconds
Finally, we can calculate the vertical drop (d) using the time (t) and acceleration due to gravity (g = 32.2 ft/s^2):
d = 1/2 * 32.2 ft/s^2 * (0.408 s)^2
d ≈ 2.11 feet
Therefore, the ball will drop approximately 2.11 feet.