Page 155 - How To Solve Word Problems In Calculus

Supplementary Problems

1. A ladder 10 ft long is resting against the side of a building. If the foot
of the ladder slips away from the wall at the rate of 2 ft/min, how
fast is the angle between the ladder and the building changing when
the foot of the ladder is 6 ft away from the building?
2. Two sides of a triangle are 3 in and 4 in long. If the angle between
them is increasing at the rate of 2 per second, how fast is the area
◦
of the triangle increasing when the angle is 45 ?
◦
3. A television camera is located 5000 ft from the base of a rocket
launching pad. The camera is designed to follow the vertical path of
the rocket. If the rocket’s speed is 500 ft/sec when it has risen
2000 ft, how fast is the camera’s angle of elevation changing at this
instant?
4. A lighthouse is situated 2 km away from a beach and its beacon
revolves at the rate of 3 revolutions per minute. If P is the point on
the beach nearest the lighthouse, how fast is the beam of light
moving along the beach when it is 1 km from P ?
5. Two corridors of widths a and b intersect at right angles. What is
the length of the longest pipe that can be carried horizontally
around the corner?
6. A painting of height 3 ft hangs on a wall with the bottom of the
painting 6 ft above the floor. How far from the wall should Lindsay,
whose eyes are 5 ft from the floor, stand in order to get the best
view of the painting? (The best view occurs when the angle of vision
from the bottom to the top of the painting is maximized.)

Solutions to Supplementary Problems

1.

θ

y 10

x

142