Page 73 - How To Solve Word Problems In Calculus

4. A baseball diamond is a square whose sides are 90 ft long. If a batter
hits a ball and runs to first base at the rate of 20 ft/sec, how fast is
his distance from second base changing when he has run
50 ft?
5. Two legs of a right triangle are each 70 cm. If one leg grows at the
rate of 5 cm/min and the other shrinks at the rate of 5 cm/min,
(a) How fast is the hypotenuse of the triangle changing 2 minutes
later?
(b) How fast is the area of the triangle changing 2 minutes later?
6. A fisherman has a fish at the end of his line, which is being reeled in
at the rate of 2 ft/sec from a bridge 30 ft above the water. At what
speed is the fish moving through the water toward the bridge when
the amount of line out is 50 ft? (Assume the fish is at the surface of
the water and there is no sag in the line.)
3
7. Sand is being dumped from a dump truck at the rate of 10 ft /min
and forms a pile in the shape of a cone whose height is always half
its radius. How fast is its height rising when the pile is 5 ft
high?
8. A radar station is 2000 ft from the launch site of a rocket. If the
rocket is launched vertically at the rate of 500 ft/sec, how fast is the
distance between the radar station and the rocket changing
10 seconds later?

Solutions to Supplementary Problems

1. Let S represent the surface area of the sphere.

r

2
(a) The surface area of a sphere is S = 4πr .
dS dr
Given: =−1 Find: when r = 3.
dt dt

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