Question

(take g= 10m s-2 in this question)
A ball moves in a vertical straight line under gravity.air resistance is negligible.the ball is projected from a point 2m above the ground with an upward speed of 3ms -1
A find the time taken for the ball to reach its greatest hight above the ground.
B show that this maximum hight above the ground is 2.45m.

Answer 1

Question#18998

(take $g = 10m$ s⁻² in this question)

A ball moves in a vertical straight line under gravity. Air resistance is negligible. The ball is projected from a point $2m$ above the ground with an upward speed of 3ms⁻¹

A find the time taken for the ball to reach its greatest height above the ground.

B show that this maximum height above the ground is $2.45m$.

Solution:

Let:

$$H_0 = 2\,m$$ $$V_0 = 3\,m/s$$ $$g = 10\,m/s^2$$ $$t - ?, H_{\max} - ?$$

A.

$$V = V_0 - g\,t, \quad V = 0, \quad V_0 = g\,t, \quad t = \frac{V_0}{g}$$ $$t = \frac{3}{10} = 0.3\,s$$

B.

$$H_{\max} = H_0 + \frac{1}{2} g\,t^2$$ $$H_{\max} = 2 + \frac{1}{2} \cdot 10 \cdot 0.3^2 = 2.45\,m$$