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 trajectory of the pitch. The relationship between speed, distance, and drop can be explained using basic principles of physics.
First, it's important to note that the distance the ball travels horizontally (60.5 feet) is not affected by the force of gravity. This is because gravity only acts vertically, pulling the ball downward.
To find out how much the ball will drop vertically, we need to calculate the vertical distance the ball would have covered during the time it took to travel horizontally. This can be done using the concept of time of flight.
The time of flight can be calculated as:
Time = Distance / Speed
In this case, the distance is 60.5 feet and the speed is given as 101 mph. However, it's important to convert the speed from mph to feet per second for consistent units. 1 mph is approximately equal to 1.47 feet per second.
So, the speed in feet per second is:
101 mph * 1.47 ft/s/mph = 148.47 ft/s
Now we can calculate the time of flight:
Time = Distance / Speed
Time = 60.5 ft / 148.47 ft/s
Time ≈ 0.407 seconds
Since the ball is subject to the force of gravity during this time, it will drop vertically due to gravity's acceleration (approximately 32.2 ft/s²). Therefore, to find the drop, we can use the equation of motion:
Drop = 0.5 * acceleration due to gravity * (time of flight)²
Using the values:
Drop = 0.5 * 32.2 ft/s² * (0.407 s)²
Drop ≈ 2.12 feet
So, the ball will drop approximately 2.12 feet during its travel of 60.5 feet at a speed of 101 mph.