A street light is at the top of a 10 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path.

a. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole?

b. How fast is the shadow lengthening?

A man is sipping soda through a straw from a conical cup, 15 cm deep and 8 cm in diameter at the top. When the soda is 10 cm deep, he is drinking at the rate of 20 cm3 /s. How fast is the level of the soda dropping at that time?

Sand pouring from a hopper at a steady rate forms a conical pile whose height is observed to remain twice the radius of the base of the cone. When the height of the pile is observed to be 20 feet, the radius of the base of the pile appears to be increasing at the rate of a foot every two minutes. How fast is the sand pouring from the hopper?

A light is on the ground 40ft from a building. A man 6ft tall walks from the light towards the building at 6ft/s. How rapidly is his shadow on the building becoming shorter when he is 20ft from the building?

A tightrope is stretched 30 feet above the ground between the Jay and Tee buildings which are 50 feet apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 70 feet above point A.

a. How fast is the shadow of the tightrope walker’s feet moving along the ground when she is midway

between the buildings? b. How far from point A is the tightrope walker when the shadow of her feet reaches the base of the Tee

Building? c. How fast is the shadow of the tightrope walker’s feet moving up the wall of the Tee Building when she is

10 feet from point B?

JayTee

A ball is dropped from a height of 64 feet and at a horizontal distance of 16 feet from a light that is 64 feet above the ground at the top of a light pole. How fast is the shadow of the ball moving along the ground one second after the ball is dropped? Neglect air resistance so that the distance the football will have dropped as a function of time will be s = 16t2 with the football dropped at t = 0.

Water is leaking out of an inverted conical tank at a rate of 10500 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank.

http://www2.scc-fl.edu/lvosbury/images/LamppostManA.gif

A man 6 feet tall is walking toward a lamppost 20 feet high at a rate of 5 feet per second. The light at the top of the lamppost (20 feet above the ground) is casting a shadow of the man. At what rate is the tip of his shadow moving and at what rate is the length of his shadow changing when he is 10 feet from the base of the lamppost?