Question

A ball of mass 10 gram is dropped from a height of hundred metre, after striking the ground 25% of kinetic energy decreases. how much height the ball will attend after striking the ground?​

Answer 1

Explanation:

Given,

M = 10g = 0.01kg

h = 100m

After striking the ground 25% of kinetic energy decreases.

To Find,

How much height the ball will attend after striking the ground?

Solution,

\begin{gathered}:\implies Kinetic \: \: Energy = Mgh \: \: (g = 10m {s}^{ - 2} ) \\ \\ :\implies Kinetic \: \: Energy = 0.01kg \times 10m {s}^{ - 2} \times 100m \\ \\ :\implies Kinetic \: \: Energy = 10J\end{gathered}

:⟹KineticEnergy=Mgh(g=10ms

−2

)

:⟹KineticEnergy=0.01kg×10ms

−2

×100m

:⟹KineticEnergy=10J

After striking the ground 25% of kinetic energy decreases.

So,

75% of Kinetic Energy remains

\begin{gathered}:\implies 75 \: percent \: \: of \: \: 10J \\ \\ :\implies \frac{75}{100} \times 10J \\ \\:\implies 7.5J\end{gathered}

:⟹75percentof10J

:⟹

100

75

×10J

:⟹7.5J

Required Answer,

\begin{gathered}:\implies Kinetic \: \: Energy = 7.5J \\ \\:\implies Mgh = 7.5J \\ \\:\implies 0.01kg \times 10m {s}^{ - 2} \times h = 7.5J \\ \\:\implies 0.1kgm {s}^{ - 2} \times h = 7.5J \\ \\ :\implies h = \frac{7.5J}{0.1kgm {s}^{ - 2} } \\ \\ :\implies h = 75m\end{gathered}

:⟹KineticEnergy=7.5J

:⟹Mgh=7.5J

:⟹0.01kg×10ms

−2

×h=7.5J

:⟹0.1kgms

−2

×h=7.5J

:⟹h=

0.1kgms

−2

7.5J

:⟹h=75m

Height = 75m

Answer 2

Given,

• M = 10g = 0.01kg
• h = 100m
• After striking the ground 25% of kinetic energy decreases.

To Find,

• How much height the ball will attend after striking the ground?

Solution,

$\begin{gathered}:\implies Kinetic \: \: Energy = Mgh \: \: (g = 10m {s}^{ - 2} ) \\ \\ :\implies Kinetic \: \: Energy = 0.01kg \times 10m {s}^{ - 2} \times 100m \\ \\ :\implies Kinetic \: \: Energy = 10J\end{gathered}$

After striking the ground 25% of kinetic energy decreases.

So,

75% of Kinetic Energy remains

$\begin{gathered}:\implies 75 \: percent \: \: of \: \: 10J \\ \\ :\implies \frac{75}{100} \times 10J \\ \\:\implies 7.5J\end{gathered}$

Required Answer,

$\begin{gathered}:\implies Kinetic \: \: Energy = 7.5J \\ \\:\implies Mgh = 7.5J \\ \\:\implies 0.01kg \times 10m {s}^{ - 2} \times h = 7.5J \\ \\:\implies 0.1kgm {s}^{ - 2} \times h = 7.5J \\ \\ :\implies h = \frac{7.5J}{0.1kgm {s}^{ - 2} } \\ \\ :\implies h = 75m\end{gathered}$

$Height = 75m$