Question

A stone is dropped from a height of 1 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

A stone is dropped from a height of 1 km. the distance it falls through varies directly with the square of the time taken to fall through that.
e.g., $S\propto t^2$

S = kt² , where k is proportionality constant.
it travel 64m in 4 sec.
put S = 64, t = 4
then, 64 = k(4)² => k = 4

hence, equation is S= 4t²
we have to find distance covered in 5th second.
e.g., $S_{5th}=|S(t=5)-S(t=4)|$
$= |4(5)^2-4(4)^2|$
= 100 - 64
= 36m

hence, distance travelled in 5th sec is 36m.
therefore, option (d) is correct.

Answer 2

D. is correct the correct answer

S = kt² , where k is constant.

travel 64m in 4 sec.

put S = 64, t = 4

Substitute for 64 = k (4)² => k = 4

Hence, equation is S= 4t²

we have to find distance covered in 5th second.

e.g.,

= 100 - 64

= 36m