Question

professional baseball player nolan ryan could pitch a baseball at approximately 160.0 km/h. at that average velocity, how long did it take a ball thrown by ryan to reach home plate, which is 18.4 m from the pitcher’s mound? compare this with the average reaction time of a human to a visual stimulus, which is 0.25 s.

Answer 1

Answer:

0.41 s

Explanation:

Parameters given:

Speed of ball, v = 160 km/h

Distance between Ryan and the home plate, d = 18.4 m = 0.0184 km

Speed is given as the time rate of change of distance. Mathematically:

$Speed = \frac{distance}{time} \\\\\\v = \frac{d}{t}$

Therefore, time will be:

$t = \frac{d}{v}$

$t = \frac{0.0184}{160} \\\\\\t = 0.000115 hr = 0.41 s$

The time it will take the ball to reach the home plate is 0.41 s.

Comparing this to the average reaction time of humans to visual stimulus (0.25 s), we see that the time it will take the ball is greater than the reaction time.

This implies that an average person should be able to track the motion of the ball as it moves towards the home plate.

Answer 2

Answer:

t = 0.4 s

Explanation:

Assuming that we can neglect the influence of gravity, the ball travels at a constant speed along a straight line, between the pitcher's mound and the home plate.

We can apply the definition of average velocity, as follows:

v = xf-xo /tfin-to

If we choose to = 0, and xo = 0 (coincident with the mound's  location), we can simply put:

t = xf / v (1)

As we have x and v in different units, we can convert v from km/h to m/s, as follows:

v= 160 Km/h * (1 h/ 3600 sec) * (1000 m / 1 Km) = 44.4 m/s

Replacing in (1):

t = 18.4 m / 44.4 m/s = 0.4 s

As the average reaction time of a human to a visual stimulus, is roughly 0.25 sec, the time needed for the ball to travel is just 1.25 of this time.