Question

- A body is projected vertically upwards with a given
velocity. The ratio of the times taken to cover the first
one fourth and the last one fourth of the ascent to the
highest point is
(a) 1:2-√3 (b) 2:2-√3
(c) 2-√3:1 (d) 2-√3:2​

Answer 1

Answer:

Option c) (2−√3):1

Explanation:

So, the time taken by the body to cover the second half of the journey will be that S=1/2gt2^2 or here the value of S=h/4 so, the value of the time will be t2=√  [2(h/4)/g].

or the value of the t2=√  [h/2g].

Again, the first half  of the journey or the first one fourth of the journey can be calculated by the following expression t1=√  [2h/g] - √  [2(3h)/g].

So, now t1 on solving we will get that h/2g is common so then the rest portion will be :-

t1=√h/2g  [2-√3].

So, the ratio of t1:t2=(2−√3):1.