Question

if a body is thrown up with an initial velocityu and covers a maximum height of h, then his equal to:​

Answer 1

To derive an expression for the maximum height 'h', we have to consider vertical motion of the body only.

Generally the initial velocity is u, but for vertical motion the initial velocity is the vertical component of u, i.e., u sin θ, where θ is the angle of inclination of the velocity with the horizontal.

Here acceleration is '-g'. Well, 'g' is towards the earth, i.e., downwards.

At maximum height, velocity, v = 0.

Now, we have the third equation of motion,

v² = u² + 2as

s = (v² - u²) / 2a

Here, v = 0, u is replaced by u sin θ, a = - g and s = h.

h = (0 - (u sin θ)²) / (- 2 g)

h = u² sin² θ / 2g