Chapter 11.4, Problem 51PPS

To determine

Find the total distance travelled.

Answer to Problem 51PPS

The ball travelled 200 feet.

Explanation of Solution

Given:

In a physics experiment, a steel ball on a flat track is accelerated and then allowed to roll freely. After the first minute, the ball has rolled 120 feet. Each minute the ball travels only 40% as far as it did during the preceding minute. How far does the ball travel?

Concept Used:

The distance the ball travels in the minutes after it rolls freely from a geometric series.

After the first minute, the ball has rolled feet. So, $a_1=120$

Each minute the ball travels only 40% as far as it did during the preceding minute.

So, $r=40\%=0.40$

Calculation:

The distance the ball travels in the minutes after it rolls freely from a geometric series.

After the first minute, the ball has rolled feet. So, $a_1=120$

Each minute the ball travels only 40% as far as it did during the preceding minute.

So, $r=40\%=0.40$

Use the infinite series sum formula: $S=\frac{a_1}{1-r}$

Now substitute: $a_1=120;r=0.40$

  $\text{S}=\frac{a_1}{1-r}=\frac{120}{1-0.40}=\frac{120}{0.60}=200$

Thus, the ball travelled 200 feet.