Last night Mookie Betts hit a baseball at 32.5 m/s at a 45° angle. Betts hit it from a height of 1m and the right field fence where he hit the ball

towards is 3m tall and 99m away. Was this hit a home run? How far did

it go?

a) Since the height of the baseball at 99 m was 8.93 m and the fence at that distance is 3m tall, the hit was a home run.

b) The total distance traveled by the baseball was 108.7 m.

Explanation:

a) To know if the hit was a home run we need to calculate the height of the ball at 99 m:

Where:

: is the final height =?

: is the initial height = 1 m

: is the initial vertical velocity = v₀sin(45)

v₀: is the initial velocity = 32.5 m/s

g: is the gravity = 9.81 m/s²

t: is the time    

First, we need to find the time by using the following equation:

Now, the height is:

Since the height of the baseball at 99 m was 8.93 m and the fence at that distance is 3m tall, the hit was a home run.

b) To find the distance traveled by the baseball first we need to find the time of flight:

By solving the above quadratic equation we have:

t = 4.73 s

Finally, with that time we can find the distance traveled by the baseball:

Hence, the total distance traveled by the baseball was 108.7 m.

I hope it helps you!