Question 87: Motion in 1D

Question

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the
particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation
between H, u and n is:

Accepted Answer

Time taken to reach highest point is $$t = {u \over g}$$
Time taken by the particle to reach the ground = $$nt = {nu \over g}$$
Speed on reaching ground $$v = \sqrt {{u^2} + 2gH} $$
Now, $$v = u + at$$
$$ \Rightarrow \sqrt {{u^2} + 2gH}  =  - u + gt$$
$$ \Rightarrow t = {{u + \sqrt {{u^2} + 2gH} } \over g} = {{nu} \over g}$$  (from question)
$$ \Rightarrow 2gH = n\left( {n - 2} \right){u^2}$$

Answer

2gH = n
2
u
2

Answer

gH = (n - 2)
2
u
2

Answer

2gH = nu
2
(n - 2)

Answer

gH = (n - 2)u
2

Motion in 1D

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

Choose the correct answer: