Question

A particle p1 is projected vertically upwards from horizontal ground, with a speed of 30m/s.At the same constant another particle p2 is projected vertically upwards from the top of a tower of height 25m,with a speed of 10m/s. Find the time for which p1 is higher than the top of the tower

Answer 1

$$h_1=v_1t-0.5gt^2$$

$$h_1-h=v_1t-0.5gt^2-h=30t-5t^2-25$$

$$30t-5t^2-25=0$$ $$t_1=1\ s$$

$$t_2=5\ s$$

p₁ is higher than the top of the tower between these values. The related time is

$$\Delta t=t_2-t_1=5-1=4\ s$$