A boat is pulled into a dock by means of a winch 12 feet above the deck of the b

Question

A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat.
(a) The winch pulls in rope at a rate of 4 feet per second. Determine the speed of the boat when there is 37 feet of rope out
What happens to the speed of the boat as it gets closer to the dock

A (square) baseball diamond has sides that are 90 feet long. A player 26 feet from third base is running at a speed of 21 feet per second. At what rate is the player's distance from home plate changing? (Round your answer to two decimal places.)

A man 6 feet tall walks at a rate of 6 feet per second away from a light that is 15 feet above the ground

when he is 10 feet from the base of the light, what rate is the tip of his shadow moving?
when he is 10 feeet from the base of the light at what rate if the length of his shawdow changing?

Explanation / Answer

(a) a= distance from dock,b = height of dock,c = length of rope

so by using the rule of right triangle to get the distance from dock

a2+b2=c2

so a = 35

also a2+b2=c2

2ada/dt+2bdb/dt=2cdc/dt

35da/dt+12(0)=37(4)

so da/dt = 4.228ft/sec

as it gets closer to dock,the speed of boat will decrease, because there is less rope to pull.

2.x= distance from player to 3rd base
d= dis. from player to home plate

using pythogoras theorem

d2=902+x2

as x = 26

d= (8100+676)1/2=(8776)1/2

player is running at a speed of 21feet/sec toward home,so it is negative

so dx/dt =-21

using pythogoras again

d2=902+x2

dd(d)/dt=xdx/dt

dd/dt=(26/(8776)1/2)(-21)=5.82ft/sec

so distance is changing at a rate of 5.82 ft/sec

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