HELP: Mechanics M1 question; how to solve?

[examman]

Hi, I'm having trouble figuring out how to solve this question.

"A particule is projected vertically upwards witha speed of 30m/s from a point A. The point B is h meters above A. The particle moves freely under gravity and is above B for a time 2.4s calculate the value of h."

Answer is supposed to be 39 meters (correct to 2 significant figures)
This question is in page 35 of Mechanics M1: Edexcel AS and A Level Modular Mathematics.

Can anyone help me solve this?

 

[VelaneDeBeaute]

First divide the journey of the particle in two pieces. Let one be from A to B and the other one from B to its maximum height and then again to B(in the figure this is from B to C, but its the same thing). Now use the formula 2as = v^2 - u^2 for the journey from A to B. Remember to take the acceleration negative. You'll end up with the speed of the particle at B, which will be this :
v = (underroot)(900-19.62h)
Now for the second part of the journey, the motion from B to B, you apply the formula s = ut + 1/2at^2. Acceleration whether negative or positive will have no effect whatsoever. The speed at B which we did find initially will replace u here. Time is given as 2.4sec, and s = 0 metres because the particle is where it was initially. The equation will give you the value of h, on solving, as 38.8 which is 39m, correct to 2 sig fig.