Question

A ball is thrown vertically downwards from a height of \(30\) m with initial velocity \(V_{0}\). It collides with the ground and loses \(60\ \%\) of its energy in collision and rebounds to \(20\) m. The initial velocity \(V_{0}\) is (\(g=10\ \text{m/s}^{2}\)).

• A. \(20\) m/s
• B. \(10\) m/s
• C. \(30\) m/s
• D. \(40\) m/s

Hint:

Equate the energy left after the collision to the energy needed to rise to 20 m, using the initial energy at 30 m.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Total energy per unit mass just before impact is \(gh+\dfrac{1}{2}V_{0}^{2}\). After losing \(60\%\), only \(40\%\) of it remains.

Step 2: Energy after the collision
The ball rebounds to \(20\) m, so the energy per unit mass after the collision is \(g\times20=200\ \text{J/kg}\).

Step 3: Calculation
\(0.4\left(300+\dfrac{1}{2}V_{0}^{2}\right)=200\)
\(300+\dfrac{1}{2}V_{0}^{2}=500\), so \(V_{0}^{2}=400\) and \(V_{0}=20\ \text{m/s}\).

Final Answer:
The initial velocity is 20 metres per second. \[ \boxed{\text{(A) }20\ \text{m/s}} \]