Question

The time of flight of a ball thrown horizontally change if the initial velocity change? If it does why?

Answer 1

From equation of motion in horizontal direction:

S_x = u_x *t + 1/2* a_x *t²                                    ( u = initial velocity)

R   = u_x * t + 0                     -------------1 ( since velocity is constant in horizontal direction)

R = range = maximum distance covered by ball in horizontal direction.

In vertical direction:

S_y= u_y *t + 1/2*a_y *t²                           ( h = maximun height, T = time of flight)

h = 0 + 1/2* g*T²

T = (2h/g)^1/2                   -----------------------2

from equation 2 , since initial velocity in vertical direction is zero and it has acceleration =g

time of flight ( T) does not depend on initial velocity .It depends on maximum height covered.

So if we change the initial velocity time of flight will not change.

But if we talk about horizontal range R , it will increases if we increases the initial velocity , as from eq. 1.