A man starts walking north at 5 ft/s from a pout P. Five minutes later a woman s

Question

A man starts walking north at 5 ft/s from a pout P. Five minutes later a woman starts working south at 7 ft/s from a point 500 people moving apart 15 min after the woman starts walking? (Round your answer to two decimal places.) A baseball diamond Is a square with side 90 ft. A better hits the ball and runs toward first base with a speed of 25 ft/s. At what rate is his distance from second base decreasing when he is halfway to first (Round your answer to one decimal place.) At what rate is his distance from third base increasing at the same moment? (Round your answer to one decimal place.)

Explanation / Answer

Answer -2

A) x = distance between batter and first base
r = distance between batter and second base
r² = x² + 90²
Halfway to first base, x = 45 ft.
r² = 45² + 90²
r = 100.62 ft
2r(dr/dt) = 2x(dx/dt)
r(dr/dt) = x(dx/dt)
(100.62 ft)(dr/dt) = (45 ft)(-25 ft/s)
dr/dt = - 11.18 ft/s
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B) Third base is at (0 , 90)
Distance = sqrt ( 90^2 + x^2 )
dD/dt = dD/dx * dx/dt
dD/dx [ sqrt ( 90^2 + x^2 ) ] = x / sqrt(x^2 + 8100)
dD/dt = 45 / sqrt(45^2 + 8100) * 25
dD/dt = 11.18
Distance to third is increasing at 11.18 feet / second

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