Related Rates Applets
http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_app_rr_oil_slick.html
The radius of a circular oil slick expands at a rate of 2 m/min.
1. How fast is the area of the oil slick increasing when the radius is 25 m?
2. If the radius is 0 at time t = 0, how fast is the area increasing after 3 min?
http://www.calculusapplets.com/snowballproblem.html
A snowball with radius 70cm is melting so that its radius is shrinking at a constant velocity of 2cm/minute.
1. Find the rate the snow ball is shrinking when the radius is 20 cm
2. Find the rate the snow ball is shrinking at time t = 10
http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_app_rr_car.html
One mile from a house, down a straight road, is an intersection. A highway runs through the intersection, perpendicular
to the road to the house. Suppose an automobile travels 60 mph along the highway. How fast is the distance between
the car and the house increasing when the car is 3 miles past the intersection?
http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_app_rr_falling_ladder.html
A 16-ft ladder leans against a wall.
1. If the bottom of the ladder moves away from the wall at a constant rate, how would you describe the
movement of the top of the ladder?
2. If the distance from the bottom of the wall to the bottom of the ladder is increasing, is the height of the ladder,
dh
, positive or negative?
dt
3. Suppose the bottom of the ladder is 5 ft from the wall at time t = 0 and it slides away from the wall at a constant
rate of 3 ft/s. Find the velocity of the top of the ladder at time t = 1.
4. Suppose the top of the ladder slides down at a constant rate of 4 ft/s. Calculate
dx
when h = 12, where x is the
dt
distance from the bottom of the wall to the bottom of the ladder.
http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_app_rr_trains.html
One train travels west toward Denver (the origin) at 2 mi/min (120 mph), while another train travels north away from
Denver at 1.5 mi/min (90 mph). At time t = 0 (here t is in minutes) the first train is 20 miles east of Denver and the
second train is 10 miles north of Denver.
1. Calculate the rate at which the distance between the trains is changing when t = 0.
2. Calculate the rate at which the distance between the trains is changing when t = 10.
3. Look at your answer to the previous question and see how it relates to the situation modeled in the applet.
Could you have guessed your answer without doing any calculation?
http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_app_rr_streetlamp.html
A boy on a skateboard rolls away from a 15-ft lamppost at a speed of 3 ft/s. The boy's height on the skateboard is 6 feet.
1. Find the rate at which his shadow is increasing in length.
2. Find the speed at which the tip of his shadow is moving.
http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_app_rr_conical_tank.html
Water pours into a conical tank with radius 4 and height 10 at a constant rate of 10 ft³ per minute. How fast is the water
level rising when it is 5 feet high?
http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_app_rr_searchlight.html
A searchlight rotates at a rate of 3 revolutions per minute. The beam hits a wall 10 miles away and produces a dot of
light that moves horizontally along the wall. How fast is this dot moving when the angle between the beam and the line
through the searchlight perpendicular to the wall is
π
6
?
http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_app_rr_rocket.html
A rocket travels vertically from a launch pad 10 km away from an observer with a telescope. At a certain moment the
angle between the telescope and the ground is
velocity (in km/min) at that moment?
π
3
and it is changing at a rate of 0.5 rad/min. What is the rocket's