Bouncy Ball

Classical Mechanics Level 3

A ball is thrown downward with initial speed v v from a height of 10 m. It loses 50% of its kinetic energy after striking the floor. It reaches to the same height after collision. What is the value of v v ?

Image Credit: Wikimedia MichaelMaggs .
It is never possible 28 m/s 14 m/s 7 m/s

Manish Dash by Manish Dash , 22, India

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2 solutions

Ivander Jonathan
Jul 9, 2015

We assume g = 9.8 m / s 2 g=9.8 m/s^2 , and mass m m

Potential Energy at 10m : P E = m g h = ( 9.8 ) ( 10 ) ( m ) = 98 m PE=mgh=(9.8)(10)(m)=98m

Kinetic energy caused by v : K E = 1 2 m v 2 KE=\frac{1}{2}mv^2

Sum of energy when reaching the floor :

Σ E = P E + K E = ( 98 + 1 2 v 2 ) m \Sigma E=PE+KE=(98+\frac{1}{2}v^2)m → \rightarrow This will be reduced 50%.

Because it reaches 10m again : 98 m = 1 2 ( 98 + 1 2 v 2 ) m 98m=\frac{1}{2}(98+\frac{1}{2}v^2)m

Which gives us v = 14 m / s 2 v=14m/s^2

8 Helpful 0 Interesting 0 Brilliant 0 Confused
Kafi Shabbir
Feb 5, 2016

zello, mechanical energy is not halved, kinetic energy is halved, the answer is 14.9

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Well, the ball loses its energy when it strikes the floor. So mechanical energy at that point is only kinetic energy as potential energy is 0 (Bcoz height is 0) . So at that point, kinetic energy getting halved essentially means the mechanical energy getting halved..... i hope i'm right

Siddhant Chaudhari - 5 years, 4 months ago

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