Question

An object was thrown straight up to land on a platform of 3.2 m high. What isthe least initial velocity needed from the ground level to do this? (using g9.81 ms 2).

Answer 1

7.95 m/s

Step-by-step explanation

The least initial velocity is the one for which when the object reaches the height of the platform its velocity is zero. From the velocity equation we have,

`v=v_o-gt`

If v = 0,

`v_o=gt`

To find the velocity we have to find the time. From the displacement equation,

`y=v_ot-(1)/(2)gt^2`

Replace v0 by the expression above,

`\begin{gathered} y=gt^2-(1)/(2)gt^2 \\ y=(1)/(2)gt^2 \end{gathered}`

We know that the height of the platform is 3.2m. Solving this equation for t,

`t=\sqrt[]{(2y)/(g)}=\sqrt[]{(2\cdot3.2m)/(9.81m/s^2)}\approx0.81s`

If the object is in the air for 0.81 seconds before reaching the platform, its initial velocity is,

`v_o=gt=9.81m/s^2\cdot0.81s=7.95m/s`

The least initial velocity needed from ground level for the object to reach the platform is 7.95 m/s