If a particle of mass m is launched vertically upwards from the ground with velocity u m/s, how long will it take to return to the ground in terms of m, u and g?
Taking upwards to be positive, and using the 'suvat' equation s=ut+1/2at2 we know that u=u, a=-g and s=0 when the particle returns to the ground. Then we solve for t:
0=ut-1/2gt20=t(u-1/2gt)
So the particle is at the ground at t=0 or t=2u/g. Since we know the particle starts at the ground (t=0) we must have that it takes 2u/g seconds to return to the ground
