Astreet light is mounted at the top of a 15-ft-tall pole. a man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. how fast is the tip of his shadow moving when he is 30 ft from the pole?

2.67 ft/s

Explanation:

1) The diagram with the triangle that represents the situation is in the image attached.

2) Similarity properties

(x + y) / 15 = y/6

⇒ 6(x+y) = 15y

⇒ 6x + 6y = 15y

⇒ 6x = 15y - 6y

⇒ 6x = 9y

⇒ y = 6x / 9

⇒ y = 2x / 3

3) Velocity is the derivative respecto to time. Then, find the derivative respect to time, t, on both sides

dy/dt = (2/3)dx/dt

4) The statement tells v = dx/dt = 4 ft/s

⇒ dy/dt = (2/3) 4 ft/s = (8/3)m/s ≈ 2.67 ft/s

Notice that this speed is constant, it does not depends upon the distance of 30 ft.

the chart show the masses and velocities of two colliding objects that stick together after a collision.

according to the law of conservation of momentum, the momentum of the object after the collision is  

answer

1,500

kg • m/s.