Related Rates

Related Rates - Word Problems


A 13 feet13\text{ feet} long ladder is leaning against a wall and sliding toward the floor. If the foot of the ladder is sliding away from the base of the wall at a rate of 17 feet/sec,17\text{ feet/sec}, how fast is the top of the ladder sliding down the wall (in feet/sec) when the top of the ladder is 5 feet5\text{ feet} from the ground?

At time t=0 st=0 \mbox{ s}, the radius of a circle is equal to 19 cm19 \mbox{ cm}. The radius of the circle increases at a rate of 12 cm/s\frac{1}{2} \ \mbox{cm/s}. The rate of change of area at t=18 st=18 \mbox{ s} is equal to mπ cm2/sm\pi \ \mbox{cm}^2\mbox{/s} , where mm is a positive integer. What is the value of mm?

Throwing a stone in a calm lake forms concentric ripples, as shown in the above picture. If the radius of one ripple increases at the rate of 10cm10 \text{cm} per second, what is the rate of increase of the area of the ripple 22 seconds after a stone is thrown (in cm2/s\text{cm}^2/\text{s})?

During a rainstorm, the area of a circular pool of water increases at the rate of 4000π in2/sec.4000\pi\text{ in}^2\text{/sec}. At what rate is the radius expanding (in inches/sec) when the radius is 200 inches?200\text{ inches}?

A point is moving along the parabola x+5y2=0x+5y^2=0 toward the origin with xx-coordinate increasing at the rate of 5 units/s5\text{ units/s} and yy-coordinate positive. How fast is the point moving in terms of the remaining distance to the origin as it passes through the point (5,1)(-5,1) on the parabola?


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