Applications of Derivatives Assignment Part 2
Related Rates Problems
1. Water is running out of a conical funnel at a rate of 1 cm3/s. If the radius of the base
of the cone is 4 cm and the altitude is 8 cm, find the rate at which the water level is
dropping when it is 2 cm from the top.
2. The sides of an equilateral triangle are changing length at the rate of 0.2 cm/s. At
what rate is the area changing when the sides are 4.0 cm?
3. What is the rate of change of the surface area of a sphere when the radius of the
sphere is 3 cm and the radius is increasing at 6 cm/s?
4. A spherical ball of ice is melting at a rate of 10 cm3/s. Find the rate of change of the
radius when the ball has a radius of 5.0 cm.
5. A bug is approaching a 12 foot high wall along the ground at a constant rate of 3 ft/s.
What is the rate of change of its distance from the top of the wall when it is 6 ft from
the bottom of the wall?
6. A television camera is located on the ground 16 km away from a point where a rocket
is to be launched vertically. At what rate is the distance between the camera to the
rocket increasing at the instant the rocket is 14 km high if the rocket’s vertical speed
is 3.0 km/s.
7. A 13ft. ladder is leaning against a house, when its base starts to slide (horizontally)
away from the wall. By the time it is 12 ft from the house, the base is moving at a
rate of 5ft/s.
a.) How fast is the top of the ladder sliding down the wall at that moment?
b.) At what rate is the area of the triangle formed by the ladder, wall and
ground changing at that moment?
c.) At what rate is the angle between the ladder and the ground changing
at that moment?
8. Sand is being dropped onto a conical pile at a rate of 10 m3/min. If the height of the
pile is always 3 times the base radius, at what rate is the height of the pile increasing
when the pile is 17 m high?
L’Hopital’s Rule
9.
Use L’Hopital’s Rule to evaluate lim
x→0
1 + x −1−
x2
x
2