Question

Bill runs around the perimeter of a circular track at 11 ft/sec. The track has a radius of 110 yd. After 24 seconds, Bill turns and runs to the center of the track along a straight (radial) line. Upon reaching the center, he turns and runs away along a different radial line to his starting position on the perimeter. Assume Lee does not slow down when he makes these two turns.

Required:
a. Sketch a picture of the situation.
b. How far has Lee traveled once he returns to his starting position?
c, How much time will elapse during Lee's circuit?
d. Find the area of the pie shaped sector esclosed by Lee's path.

Answer 1

Explanation:

We can see the sketch of the diagram in the image attached below.

Since 1 yard =3 feet

110 yards = 330 feet

Using: Distance = speed * time

If the speed of Lee is 11 ft/sec, he will travel the distance = 11 ft/sec * 24 sec = 264 ft in 24 sec.

The distance traveled = 264 ft

After traveling 264 ft, he takes a turn radially towards the center, then again takes a turn as he reaches the center.

b)

Total Distance traveled = A + B + C

A = C = 330 ( radius of the circle)

= 330 + 110 + 330

= 770 ft

c) Using the expression:

Speed = Distance/time

time = Distance/Speed

time = 770/11

time = 70 sec

d)

Area = 1/2 r²θ

Area = 1/2 r² (l/r)

Area = 1/2 × r × l

Area = 1/2 × 330 × 110

Area = 18150 ft²