Problem 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.
Problem 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?
Problem 08
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?
Problem 06
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.
Problem 04
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.
Problem 03
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.
Problem 01
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?
Problem 02
Water flows into a vertical cylindrical tank at 12 ft3/min, the surface rises 6 in/min. Find the radius of the tank.
Time Rates
If a quantity x is a function of time t, the time rate of change of x is given by dx/dt.
When two or more quantities, all functions of t, are related by an equation, the relation between their rates of change may be obtained by differentiating both sides of the equation with respect to t.
Maxima and minima
Time Rates
Problem 675
Repeat Prob. 674 for the overhanging beam shown in Fig. P-675.
