1. Water is flowing into a vertical cylindrical tank at the
rate of 24 ft3/min. If the radius of the tank is 4 ft, how
fast is the surface rising?
2. Water flows into a vertical cylindrical tank at 12
ft3/min, the surface rises 6 in/min. Find the radius of the
tank.
his shadow move along the wall when he is 5 ft from the
house?
16. In Problem 15, when the man is 5 ft from the house,
find the time-rate of change of that portion of his
shadow which lies on the ground.
3. A rectangular trough is 10 ft long and 3 ft wide. Find
how fast the surface rises, if water flows in at the rate of
12 ft3/min.
17. A light is placed on the ground 30 ft from a building.
A man 6 ft tall walks from the light toward the building
at the rate of 5 ft/sec. Find the rate at which the length of
his shadow is changing when he is 15 ft from the
building.
4. A triangular trough 10 ft long is 4 ft across the top,
and 4 ft deep. If water flows in at the rate of 3 ft3/min,
find how fast the surface is rising when the water is 6 in
deep.
18. Solve Problem 17, if the light is 10 ft above the
ground.
5. A triangular trough is 10 ft long, 6 ft wide across the
top, and 3 ft deep. If water flows in at the rate of 12
ft3/min, find how fast the surface is rising when the
water is 6 in deep.
6. A ladder 20 ft long leans against a vertical wall. If the
top slides downward at the rate of 2 ft/sec, find how fast
the lower end is moving when it is 16 ft from the wall.
7. In Problem 6, find the rate of change of the slope of
the ladder.
8. A man 6 ft tall walks away from a lamp post 16 ft
high at the rate of 5 miles per hour. How fast does the
end of his shadow move?
9. In Problem 08, how fast does the shadow lengthen?
10. A boy on a bike rides north 5 mi, then turns east (Fig.
47). If he rides 10 mi/hr, at what rate does his distance to
the starting point S changing 2 hour after he left that
point?
11. A train starting at noon, travels north at 40 miles per
hour. Another train starting from the same point at 2 PM
travels east at 50 miles per hour. Find, to the nearest
mile per hour, how fast the two trains are separating at 3
PM.
12. In Problem 11, how fast the trains are separating
after along time?
13. A trapezoidal trough is 10 ft long, 4 ft wide at the
top, 2 ft wide at the bottom and 2 ft deep. If water flows
in at 10 ft3/min, find how fast the surface is rising, when
the water is 6 in deep.
14. For the trough in Problem 13, how fast the water
surface is rising when the water is 1 foot deep.
15. A light at eye level stands 20 ft from a house and 15
ft from the path leading from the house to the street. A
man walks along the path at 6 ft per sec. How fast does