Question

a free falling body crosses point P,Q and R with velocities V,2V AND 3V.find the ratio of the distance PQ to QR.

Answer 1

PQ:
On PQ the velocity changes by the law:
2V = V + gt1
Then we get the time required to move from P to Q:
t1 = V / g
Law for changing coordinate:
PQ = V * t1 + g(t1)^2 / 2 = V^2 / g + g * (V/g)^2 / 2 = V^2 / g + V^2 / 2g =
3V^2 / 2g
So PQ = 3V^2 / 2g

QR:
On PQ the velocity changes by the law:
3V = 2V + gt2
Then we get the time from Q to R:
t2 = V / g
QR = 2V * t2 + g(t2)^2 / 2 = 2V^2 / g + g * (V/g)^2 / 2 = 5V^2 / 2g
So QR = 5V^2 / 2g

Finally the ratio is: PQ / QR = (3V^2 / 2g) / (5V^2 / 2g) = 3 / 5 = 0.6.