CALCO!!
A stone dropped into a still pond
sends out a circular ripple whose
radius increases at a constant
rate of 3ft/s. How rapidly is the
area enclosed by the ripple
increasing at the end of 10 s?
Oil spilled from a ruptured tanker
spreads in a circle whose area
increases at a constant rate of
6 mi2/h. How fast is the radius of
the spill increasing when the area is
9 mi2?
A spherical balloon is inflated so that
its volume is increasing at the rate of
3 ft3/min. How fast is the diameter
of the balloon increasing when the
radius is 1 ft?
A spherical balloon is to be deflated
so that its radius decreases at a
constant rate of 15 cm/min. At
what rate must air be removed when
the radius is 9 cm?
A 17-ft ladder is leaning against a
wall. If the bottom of the ladder is
pulled along the ground away from
the wall at a constant rate of 5 ft/s,
how fast will the top of the ladder be
moving down the wall when it is 8 ft
above the ground?
A 13-ft ladder is leaning against a
wall. If the top of the ladder slips
down the wall at a rate of 2 ft/s, how
fast will the foot be moving away
from the wall when the top is 5 ft
above the ground?
A 10-ft plank is leaning against a
wall. If at a certain instant the
bottom of the plank is 2 ft from the
wall and is being pushed toward the
wall at the rate of 6 in/s, how fast is
the acute angle that the plank
makes with the ground increasing?
A softball diamond is a square whose
sides are 60 ft long. Suppose that a
player running from first to second
base has a speed of 25 ft/s at the
instant when she is 10 ft from
second base. At what rate is the
player’s distance from home plate
changing at that instant?
A rocket, rising vertically, is tracked
by a radar station that is on the
ground 5 mi from the launch pad.
How fast is the rocket rising when it
is 4 mi high and its distance from
the radar station is increasing at a
rate of 2000 mi/h?
A conical water tank with vertex
down has a radius of 10 ft at the top
and is 24 ft high. If water flows into
the tank at a rate of 20 ft3/min, how
fast is the depth of the water
increasing when the water is 16 ft
deep?
Grain pouring from a chute at a rate
of 8 ft3/min forms a conical pile
whose altitude is always twice the
radius. How fast is the altitude of the
pile increasing at the instant when
the pile is 6 ft high?
Sand pouring from a chute forms a
conical pile whose height is always
equal to the diameter. If the height
increases at a constant rate of 5
ft/min, at what rate is sand pouring
from the chute when the pile is 10 ft
high?
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An aircraft is climbing at a 30 angle
to the horizontal. How fast is the
aircraft gaining altitude if its speed is
500 mi/h?
A boat is pulled into a dock by
means of a rope attached to a pulley
on the dock. The rope is attached to
the bow of the boat at a point 10 ft
below the pulley. If the rope is
pulled through the pulley at a rate of
20 ft/min, at what rate will the boat
be approaching the dock when 125 ft
of rope is out?
A man 6 ft tall is walking at the rate
of 3 ft/s toward a streetlight 18 ft
high.
At what rate is his shadow
length changing?
How fast is the tip of his shadow
moving?