Question

You throw a small rock straight up from the edge of a highway bridge that crosses a river. The rock passes you on its way down, 6.00 s after it was thrown. After the rock hits the surface of the water it sinks into the water through a depth of 1.0 meter and reached a speed of .5 m/s. What is the rate of slowing down for the rock in the water during this 1 meter travel, assuming it slows down at a constant rate? Ignore air resistance.

Answer 1

consider the motion of the rock for first 6 sec :

Y = displacement = 0

t = 6 sec

a = acceleration = - 9.8

V_o = initial velocity of launch in up direction

using the equation

Y = V_o t + (0.5) a t²

0 = V_o (6) + (0.5) (- 9.8) (6)²

V_o = 29.4 m/s

consider the motion of the rock in water for 1 m :

Y = displacement = - 1 m

a = acceleration

V_o = initial velocity in down direction = - 29.4

V_f = final velocity = 0.5 m/s

Using the equation

V_f² = Vo² + 2 aY

(0.5)² = (- 29.4)² + 2 (- 1) a

a = 432.1 m/s²