Question

Distance(feet), x: 0, 2, 6, 9, 12, 13, 15
Height (feet) f(x): 4, 8.4, 12.1, 14.2, 13.2, 10.5, 9.8

Find the height of the ball when it traveled a distance of 10 feet.

A) 17 ft

B) 11.1 ft

C) 12.8 ft

D) 13.3 ft

Answer 1

To find the height of the ball when it traveled a distance of 10 feet, we need to determine the height for the given distances that are closest to 10 feet. The distances closest to 10 feet are 9 feet and 12 feet.

Using linear interpolation:

For x = 9 feet:
f(9) = 14.2 ft

For x = 12 feet:
f(12) = 13.2 ft

Now, we can interpolate the height at x = 10 feet:

f(10) = f(9) + (10-9) * [(f(12) - f(9))/(12-9)]
f(10) = 14.2 + (10-9) * [(13.2 - 14.2)/(12-9)]
f(10) = 14.2 + 1 * [(13.2 - 14.2)/3]
f(10) = 14.2 + 1 * [-1/3]
f(10) = 14.2 - 1/3
f(10) = 14.2 - 0.33333
f(10) ≈ 13.8667 ft

Therefore, the height of the ball when it traveled a distance of 10 feet is approximately 13.87 ft, which is closest to 13.8667 ft.

Therefore, the closest option is:

C) 12.8 ft