Question

At what vertical velocity should no object be launched at in order to achieve a height of 20m?​

Answer 1

Answer:

19.8 m/s

Explanation:

Given:

Maximum vertical displacement of the object (H) = 20 m

Acceleration due to gravity (g) = 9.8 m/s²

At maximum height, the velocity of the object is 0 m/s for a moment. So, final velocity (v) at the maximum height is 0 m/s.

Now, let the initial velocity or velocity at launch be 'u' m/s.

Now, using the following equation of motion for vertical motion:

$v^2=u^2-2gH$

Rewriting in terms of 'u', we get:

$u^2=v^2+2gH\\\\u=\sqrt{v^2+2gH}$

Plug in the given values and solve for 'u'. This gives,

$u=\sqrt{0+2\times 9.8\times 20}\\\\u=\sqrt{392}\\\\u=19.8\ m/s$

Therefore, the vertical velocity at the launch is 19.8 m/s.