Question

A particle is thrown vertically upward with a speed of u from a tower of height h. 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 :

Answer 1

Hey there !

We know that t = u / g

So let us assume t to be the time taken to reach the maximum height and T to be total time.

So According to the question,

T = n.t

So time taken to hit the ground is,

- H = uT - 1 / 2 * gT² => Equation 1

So we know that, T = nt

=> T = n * u / g

=> T = nu / g

Substituting this in Equation 1, we get,

- H = u * ( nu / g ) - g / 2 * ( nu / g )²

=> - H = ( nu² / g ) - g / 2 * ( n²u² / g² )

=> - H = ( nu² / g ) - ( n²u² / 2g )

=> - H = ( 2nu² - n²u² / 2g )

Transposing the denominator to other side we get,

=> - 2gH = nu² ( 2 - n )

Multiplying by -1 on both sides we get,

=> 2 gH = - nu² ( 2 - n )

=> 2 gH = nu² ( n - 2 )

This is the required relation.

Hope my answer helped !