Question

A stone is dropped from a height of 5 km.the distance it falls through varies directly with the square of the time taken to fall through that distance. if it travels 64m in 4 seconds, find the distance it covers in the 5th sec.
a. 24m
b.28m
c.44m
d. 36m

Answer 1

Answer:

Distance covered in 5th second = 100-64 = 36 m

Explanation:

A stone is dropped from a height of 5 km.

The distance it falls through varies directly with the square of the time

Let us suppose distance as d and time as t

$d\propto t^2$

$d=kt^2$

where, k is constant of proportionality

If a stone travels 64 m in 4 second.

d=64 and t=4

Substitute into the formula and solve for k

$64=k\times 4^2$

64=16k

k=4 m/s$^2$

We get an relation between d and t

$d=4t^2$

We need to find distance covered by stone in the 5th second.

Distance covered in 5th second = d(5)-d(4)

At t=5, d=$4(5)^2\Rightarrow 100$ m

At t=4, d=64

Distance covered in 5th second = 100-64 = 36 m

Answer 2

36 m will be the answer of this question