Download APCALC12 - Related Rates Practice.ink

APCALC12 - Related Rates Practice.ink
Related Rates
Practice Problems
1
APCALC12 - Related Rates Practice.ink
Question 1 - A rope is attached to a pulley mounted on a 15 ft tower. The end of the
rope is attached to a heavily loaded cart. A worker can pull on the rope at the base of
the tower at a rate of 2 ft/s, causing the cart to move toward the tower. How fast is the
cart approaching the tower when it is 8 ft from its base?
2
APCALC12 - Related Rates Practice.ink
Question 3 - At 2:00 pm on a certain day, Ship A is 100 km due north of ship B. At that
moment, A begins to sail due east at 15 km/h while B sails due north at 20 km/h. How
fast is the distance between them changing at 5:00 pm? Is the distance increasing or
decreasing?
3
APCALC12 - Related Rates Practice.ink
Question 4 - On another day, ships A and B meet at midnight and then sail off in
different directions, keeping an angle of 60˚ between them. A goes at 30 km/h and B
goes at 40 km/h. How fast is the distance between them when A has traveled 9 km and
B has traveled 12 km? What time is it then?
4
APCALC12 - Related Rates Practice.ink
Question 5 - Bacteria grow in circular colonies. The radius of one colony grows at 4
mm/day. How fast is its area growing a week later?
5
APCALC12 - Related Rates Practice.ink
Question 6 - An airplane with height 1000 m is flying horizontally at a velocity of 500
km/h and passes directly over a police observer. How fast is the plane receding from
the observer when it is 1500 m away (along the direct line of sight) from the observer?
6
APCALC12 - Related Rates Practice.ink
Question 7 - A prison guard tower has a light that is 300 m from a straight wall. Its light
rotates at a rate of 5 revolutions per minute. How fast is the light beam moving across
the wall at the point which is 200 m (measured from the point on the wall closest to the
tower).
7