A ball is projected vertically down with an initial velocity from a height of $$20$$ m onto a horizontal floor. During the impact it loses $$50$$% of its energy and rebounds to the same height. The initial velocity of its projection is (in$$ $$m/s) [Take g $$=$$ $$10$$ $$m/s2$$]

Question

A ball is projected vertically down with an initial velocity from a height of $$20$$ m onto a horizontal floor. During the impact it loses $$50$$% of its energy and rebounds to the same height. The initial velocity of its projection is (in$$ $$m/s)  [Take g $$=$$ $$10$$ $$m/s2$$]

Infinity Learn · Accepted Answer

Let ball is projected vertically downward with velocity v from height h
Total energy at point $A = \frac{1}{2} {mv}^{2} + mgh$

During collision loss of energy is 50% and the ball rises up to same height. It means it possess only potential energy at same level.

$50 % (\frac{1}{2} {mv}^{2} + mgh) = mgh$

$\frac{1}{2} (\frac{1}{2} {mv}^{2} + mgh) = mgh$

$v = \sqrt{2 gh} = \sqrt{2 \times 10 \times 20}$

$∴ v = 20 m / s$

Collisions

Unlock the full solution & master the concept.

A ball is projected vertically down with an initial velocity from a height of 20 m onto a horizontal floor. During the impact it loses 50% of its energy and rebounds to the same height. The initial velocity of its projection is (in m/s) [Take g = 10 m/s²]

Ready to Test Your Skills?

free study material

Collisions

Unlock the full solution & master the concept.

A ball is projected vertically down with an initial velocity from a height of 20 m onto a horizontal floor. During the impact it loses 50% of its energy and rebounds to the same height. The initial velocity of its projection is (in m/s) [Take g = 10 m/s2]

Let ball is projected vertically downward with velocity v from height hTotal energy at point A=12mv2+mghDuring collision loss of energy is 50% and the ball rises up to same height. It means it possess only potential energy at same level.50% 12mv2+mgh=mgh1212mv2+mgh=mghv=2gh=2×10×20∴v=20 m/s

Ready to Test Your Skills?

free study material

A ball is projected vertically down with an initial velocity from a height of 20 m onto a horizontal floor. During the impact it loses 50% of its energy and rebounds to the same height. The initial velocity of its projection is (in m/s) [Take g = 10 m/s²]