Question

The left fielder throws the baseball home from 60 m away. The ball's horizontal velocity is 30 m/s, and its vertical velocity is sufficient to keep it in the air until it reaches the catcher at home plate. At the same time, a base runner is running toward home plate. His velocity is 5 m/s, and he is 5 m from home plate. If the base runner's velocity stays constant and air resistance isn't a factor, which will arrive at home plate first, the base runner or the baseball?

Answer 1

The base runner

Step-by-step explanation:

To know the correct answer to the question, we shall determine the time taken for the baseball and the base runner to get to the home plate. This is illustrated below:

For the baseball:

Horizontal velocity (u) = 30 m/s

Horizontal distance (s) = 60 m

Time (t) =?

s = ut

60 = 30 × t

Divide both side by 30

t = 60 / 30

t = 2 s

Thus, it will take the baseball 2 s to get to the home plate.

For the base runner:

Horizontal velocity (u) = 5 m/s

Horizontal distance (s) = 5 m

Time (t) =?

s = ut

5 = 5 × t

Divide both side by 5

t = 5 / 5

t = 1 s

Thus, it will take the base runner 1 s to get to the home plate.

SUMMARY:

Time taken for the baseball to get to the home plate = 2 s

Time taken for the base runner to get to the home plate = 1 s

From the calculations made above, we can conclude that the base runner will arrive at the home plate first because it took him 1 s to get to the home plate whereas the baseball took 2 s to get there.