Q103P - Fundamentals Of Physics

Question

Question: If a baseball pitcher throws a fastball at a horizontal speed of 160 Km/hr, how long does the ball take to reach home plate 18.4 m away?

Step-by-Step Solution

Answer

The time taken by ball to reach home plate is $414 \text{m/s}$ . 

Given data

The speed of the ball is $160 \text{km/h}$ .

The distance of the plate is $18.4 \text{m}$ .

Understanding the speed of an object.

 

The speed of an object is defined as the rate of change of distance with time. It is a scalar quantity.

The expression for the speed is given as follows:

   $\text{Distance= Speed×Time interval}$                                      … (i)

 

Determination of time taken by ball to reach the plate.

First, convert the speed of the ball from $\text{km/h}$ to$\text{m/s}$ .

The speed of the ball can be written as, 

$$\begin{gathered} \text{Speed = 160 km/h} \\ = 160\times \frac{5}{18} \text{m/s} \\ = 44.44 \text{m/s} \end{gathered}$$

 

From equation (i), the time taken by ball is calculated as follows: 

  $$\begin{gathered} \text{Time interval = }\frac{\text{Distance }}{\text{Speed}} \\ \text{ =}\frac{18.4\text{m}}{44.44 \text{m/s}} \\ =\text{ 0.414 s } \\ = 414 \text{ms} \end{gathered}$$

 

Thus, the time taken by ball to reach home plate is $414\text{ms}$ .