Rates Review
The position function of a point on a coordinate line is given by 2
s(t) = t3 ­ 12t + 36t ­ 20, where t is measured in seconds and s(t) in centimeters. Describe the motion of the particle during the interval [­1,9].
Jan 3­11:56 AM
At 1:00 pm, ship A is 25 miles due south of ship B. If ship A is sailing west at a rate of 16 mph and ship B is sailing south at a rate of 20 mph, find the rate at which the distance between the ships is changing at 1:30 pm.
A water tank has the shape of an inverted right circular cone with an altitude of 12 ft and radius 6 ft. If water is being pumped into the tank at a rate of 10 gal/min, approximate the rate at which the water level is rising when it is 3 ft deep. (1 gal ≈ 0.1337 ft3)
Two people on bikes are at the same place. One of the bikers starts riding directly north at a rate of 8 m/sec. Five seconds after the first biker started riding north, the second starts to ride directly east at a rate of 5 m/sec. At what rate is the distance between the two riders increasing 20 seconds after the second person started riding?
Dec 14­3:21 PM
A point moves along the curve in such a way that the y­value is decreasing at the rate of 2 units per second. At what rate is the x changing when x = 4?
For a certain rectangle the length of one side is always three times the length of the other side.
a) If the shorter side is decreasing at a rate of 2 inches/minute, at what rate is the longer side decreasing?
b) At what rate is the enclosed area decreasing when the shorter side is 6 inches long and is decreasing at a rate of 2 inches/minute?
Dec 13­3:16 PM
Rates Review
Related Rates:
1) A snowball is melting at a rate of 2 ft3 per hour. If it remains spherical, at what rate is the radius changing when the radius of the snowball is 20 inches?
2) A car is traveling west on the interstate. A highway patrolman is parked 90 feet north of the interstate. The patrolman takes a radar reading and finds that the car is 150 feet from his position, and the distance separating them is increasing at a rate of 72 ft/sec. Find the speed of the car at that moment.
3) A child is standing still and flying a kite. The kite remains at an altitude of 30 feet above the child's hands while traveling parallel to the ground at a rate of 10 feet per second. When the kite is 50 feet away from the child, how fast is the kite string leaving the child's hand?
4) A car is 30 miles north of town, heading north at 25 miles per hour. At the same time, a truck is 40 miles east of town, traveling east at 50 miles per hour. At what rate is the distance between the two vehicles changing?
Dec 20­12:24 PM