Question

A pebble is thrown vertically upwards from the bridge with an initial velocity of 4.9 m/s. It strikes the water after 2 s. If acceleration due to gravity is 9.8 m/s². The height of the bridge and velocity with which the pebble strikes the water will respectively be ______.

Options

• 4.9 m, 1.47 m/s

• 9.8 m, 14.7 m/s

• 49 m, 1.47 m/s

• 1.47 m, 4.9 m/s

Answer 1

A pebble is thrown vertically upwards from the bridge with an initial velocity of 4.9 m/s. It strikes the water after 2 s. If acceleration due to gravity is 9.8 m/s². The height of the bridge and velocity with which the pebble strikes the water will respectively be 9.8 m, and 14.7 m/s.

Explanation:

For the motion of the pebble from A to B,

u = +4.9 m/s, t = 2 sec,

s = -h, a = -9.8 m/s²

`s = ut + 1/2at^2`

`-h = 4.9(2) + 1/2(-9.8)(2)^2`

-h = 9.8 - 19.6

h = 9.8 m

v = u + at

⇒ v = 4.9 + (-9.8) (2)

v = -14.7 m/s

The -ive sign indicates that the pebble's velocity is directed downhill when it strikes the water's surface.