Differential Calculus 02

• 2.83

• 3.82

• 8.23

• 5.32

2. A statue 3 m high is standing on a base of 4 m high. If an observer’s eye is 1.5 m above the ground, how far should he stand from the base in order that the angle subtended by the statue is maximum.

• 1.17

• 4.57

• 3.71

• 2.51

3. A piece of pipe is being carried down a hallway that is 18 feet wide. At the end of the hallway there is a right-angled turn and the hallway narrows down to 12 feet wide. What is the longest pipe (always keeping it horizontal) that can be carried around the turn in the hallway?

• 40.14

• 42.14

• 44.14

• 48.14

4. Two poles, one 10-m & 15-m, are 30 meters apart. A length of wire is attached to the top of each pole and it is staked to the ground somewhere between the two poles. Where should the wire be staked so that the minimum amount of wire is used?

• 12 m from the 10-m pole

• 12 m from the 15-m pole

• 10 m from the 10-m pole

• 10 m from the 15-m pole

5. Water is flowing into a conical cistern at the rate of 8 cu.m/min. If the height of the inverted cone is 12 m and the radius of its circular opening is 6 m. How fast is the water level rising when the water is 4 m deep?

• 0.6366 m/min

• 0.5455 m/min

• 0.4744 m/min

• 0.7477 m/min

6. A helicopter is rising vertically from the ground at a constant rate of 4.5 m/s. When it is 75 m off the ground, a jeep passed beneath the helicopter travelling in a straight line at a constant rate of 80 kph. Determine how fast the distance between them changing after 1 s.

• 12.32 m/s

• 14.81 m/s

• 10.32 m/s

• 11.88 m/s

7. A ladder 20 ft long leans against a vertical wall. If the top slides downward at the rate of 2 ft/sec, find how fast the lower end is moving when it is 16 ft from the wall.

• 2.0 ft/s

• 1.5 ft/s

• 2.5 ft/s

• 3.0 ft/s

8. A light is placed on the ground 30 ft from a building. A man 6 ft tall walks from the light toward the building at the rate of 5 ft/sec. Find the rate at which the length of his shadow is changing when he is 15 ft from the building.

• -4 ft/s

• -3 ft/s

• 5 ft/s

• 2 ft/s