Question

In a baseball game, a batter has hit the ball and is running at a speed of 30 feet per second. If the baseball diamond is a square with 90–foot sides, at what rate is the player's distance from home plate changing when he is 70 feet from third base?

Answer 1

Answer:

18.418 ft/s

Step-by-step explanation:

Let the distance from the player to 3rd base be x.

Let the distance from the player to home plate be y.

The side of the square is 90'.

x = 70

x² + 90² = y²

70² + 90² = y²

y = √13,000 = 114.0175

x² + 8100 = y²

Differentiate with respect to time.

2x dx/dt = 2y dy/dt

x dx/dt = y dy/dt

We are told that dx/dt is 30 ft/s.

70(30) = 114.0175(dy/dt)

dy/dt = 18.418 ft/s