Precalc Question

Question

Rocky is a horse and he is searching his master on his ranch. His master is not moving, just sitting on a rock and whistling. The whistle can be heard from up to 1 mile away. Initially, Rocky is at a point 0.8 miles south and 0.8 miles west of his master.

(a) Can Rocky hear his master’s whistling from his initial point? Justify your answer.

(b) Rocky walks at a constant speed of 4mph. He walks towards his barn, which is located 1 mile due west of his master. After walking a while he hears his master’s whistle and immediately changes direction and walks towards him (walking at the same speed). What is the total time that Rocky spends walking?

Answer 1

Draw and label a diagram!

C is the center (0, 0) of the circle where master is located

B (-1, 0) is the location of the barn

L (-0.8, -0.8) is the location of Rocky

By Pythagoras CL is 1.13137 mi.

(a) Rocky cannot hear the whistle

LB is Rocky's path to the barn

T is the point on the circle at which Rocky hears the whistle.

Determine equation of line line LB

Determine the coordinates of T (simultaneous solution to equation above and equation of circle)

Determine distance of LT

LT + 1 = miles Rocky walks.

(b) (LT + 1) / 4 = time Rocky is walking.