A particle is projected vertically upwards with a velocity of 34.3 m/s. For how long is the particle at a height of 49 m and above the point of projection?

Calculate the time to reach a height of 49 m:

S = V0 t - 1/2 g t^2

S = 34.3 t - 1/2 * 9.8 * t^2

4.9 t^2 - 34.3 t + 49 = 0

I get t = 2 and t = 5    as solutions of the quadratic.

We know that it takes v / a = 34.3 / 9.8 = 3.5 sec to reach maximum height.

So we have:

2 sec to reach 49 m

3.5 sec to reach max height

1.5 sec from 49 m to max height

1.5 sec from max height back down to 49 m

2 sec to fall from 49 m to ground

2 sec + 1.5 sec + 1.5 sec = 5 sec  to go from ground to max height and back down to 49 m

gravity

explanation: