Question

A rock is dropped from a 168-m-high cliff. How long does it take to fall (a) the first 84.0 m and (b) the second 84.0 m?

Answer 1

Answer:

Explanation:168(9.8)

By G

Answer 2

Given:

A rock is dropped from a height of 168m.

To Find:

a) time taken to fall first 84 m

b)time taken to fall second 84 m

Solution:

a) Initial velocity of rock u = 0

distance covered by block = 84 m

We firstly use third equation of motion to calculate final velocity

$v^{2} -u^{2} = 2as$

where a is acceleration = g

v is the velocity  after 84 m

s =84 m

substitute the values of u, a, s

$v^{2} =u^{2} + 2as\\\v^{2}= 2(9.81)(84)\\ v = 40.6 \frac{m}{s}$

now use first equation of motion

$v = u+ at\\v-u = at\\t = \frac{v}{a}\\ t = 4.14 seconds$

b)

now for the second half initial velocity = 40.6

distance covered = 84m

a = g

use 3rd equation of motion

$v^{2}- u^{2} = 2as$

$v^{2} = 2as +u^{2}\\ \\v^{2} = 2(9.81)(84) + (40.6)(40.6) \\\\v = 57.4 \frac{m}{s}$

use first equation of motion to calculate t

$v = u +at\\v-u = at\\t= \frac{v-u}{a}\\ t= 1.74 seconds$

Time taken to fall first 84 m is 4.14 seconds.

Time taken to fall next 84 metres is 1.74 seconds.