Question

Show that there are two values of time for which a projectile is at the same height. Also show mathematically that the sum of these two times is equal to the time of flight.

Answer 1

It can be shown with the help of equation of h = (v₀sinθ)t – 1/2 gt², where h is the height of the particle from the ground, as this equation is quadratic so it will have two solution for each h.  

• As time of flight is equal to :- 2(v₀ sinθ/g) which is equal to the sum of roots of the above equation (i.e. the sum of two times for the same height).