When we throw a tennis ball into a lake for my dog she knows that if she swims straight for it she'll take longer to get to the

Question

When we throw a tennis ball into a lake for my dog she knows that if she swims straight for it she'll take longer to get to the ball. Instead, she
runs along the beach for a short distance and then turns and swims for the ball.
Let's say we throw the ball so that it lands 15 meters out into the water and 5 meters to the right of where we're standing. Draw a picture of this scenario.
Finally, let's say that the dog runs at a rate of 2.5 meters per second and swims at a rate of 1 meters per second.
(A) If the dog were to swim directly for the ball how long will it take? Recall that distance is equal to rate multiplied by time.
Direct Swim Time =   seconds.
(B) If the dog were to run down the beach and make a 90 degree turn and then swim directly for the ball how long would it take to get to the ball?
Time for longest run and 90 degree turn to swim =  seconds.
(C) My dog is smarter than either of the answers in parts (A) or (B). She knows that there is a better solution. Let be the amount of running that she
does down the beach (clearly r is less than 5 and greater than 0). The trip has now been broken into two parts: a running leg of length x meters and a
swimming leg at some angle to the beach. What is the length of the swimming leg as a function of r?
Length of swimming leg =
(D) Write a function T(r) that expresses the total time to get to the ball in terms of how far she runs down the beach.
T(r):

Kunduz · Accepted Answer

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