Question

Initial horizontal velocity?

A long jumper takes off from a board and covers a horizontal distance of 6.7meters and achieves a maximum height of 0.6meters during the long jump.

What is the initial horizontal velocity of the jumper at take-off from the board?

Answer 1

Let `v_v` be initial vertical velocity of projection. Maximum height would be reached when vertical velocity becomes zero. Let the jumper take time `t` to attain maximum height.

Setting up kinematic expressions and noting that gravity `g=` `-9.81\ ms^-2` acts in a direction opposite to the initial direction of motion we get

`0.6=v_vt+1/2 (-9.81)t^2` ......(1)
Also
`0=v_v+(-9.81)t`
`=>v_v=9.81t`

Inserting in (1) we get

`0.6=9.81t^2-1/2 (9.81)t^2`
`=>1/2xx9.81t^2=0.6`
`=>t=+-0.35\ s` ......(2)

Ignoring negative root as time can not be negative.

Time of flight `=2t=0.7\ s`

Initial horizontal velocity `v_h=6.7/0.7=9.6\ ms^-1`