Question

For a particle projected vertically upwards under gravity travels equal distance find its projection speed

Answer 1

your question is incomplete. A complete question is -----> For a particle projected vertically upwards passes the same same height at 2sec and at 10 sec if acceleration due to gravity is 9.8m/s² find its projection speed ?

solution : Let projection speed is u

using formula , s = ut + 1/2at²

here, s = h, a = -g = -9.8 m/s²

then, h = ut - 4.9 t²

putting, t = 2 sec

then, h = u × 2 - 4.9 × 4 = 2u - 19.6

or, h = 2u - 19.6 ........(1)

putting , t = 10sec

then, h = u × 10 - 4.9 × 100 = 10u - 490

or, h = 10u - 490..........(2)

from equations (1) and (2),

10u - 490 = 2u - 19.6

or, 8u = 490 - 19.6 = 470.4

or, u = 58.8 m/s

hence, projection speed is 58.8 m/s