Question

A ball of mass 40 g is thrown upward. It reaches to the maximum height of 80 m. At what height its kinetic energy reduced by 40%?​

Answer 1

Given:

A ball of mass 40 g is thrown upward. It reaches to the maximum height of 80 m.

To find:

Height at which KE reduced by 40%.

Calculation:

First of all, let initial velocity be u :

${v}^{2} = {u}^{2} + 2as$

$\implies {0}^{2} = {u}^{2} - 2(10)(80)$

$\implies {u}^{2} = 1600$

$\implies u = \sqrt{1600}$

$\implies u = 40 \: m {s}^{ - 1}$

Now, initial KE :

$KE = \dfrac{1}{2} m {u}^{2}$

$\implies KE = \dfrac{1}{2} \times 0.04 \times {(40)}^{2}$

$\implies KE = 32 \: joule$

Now, KE is reduced by 40%.

• So, final KE = 60% (Initial KE)

$\implies KE_{f} =60\% \times 32$

$\implies KE_{f} = 19.2$

$\implies \frac{1}{2} \times 0.04 \times {v_{f}}^{2} = 19.2$

$\implies v_{f} = 30.98 \: m {s}^{ - 1}$

Now, required height will be :

${ v_{f}}^{2} = {u}^{2} - 2gh$

$\implies 960 = 1600 - 2(10)h$

$\implies \: 20h = 640$

$\implies \: h = 32 \: m$

At height 32 metres, KE will be reduced by 40%.

Answer 2

Given:

mass of ball m = 40g

maximum height Hmax = 80 m

To find:

height at which kinetic energy is reduced by 40% h =?

Explanation:

• A ball of mass 40 g is thrown upward & reaches the maximum height of 80 m.

         i.e. m = 40 g

         Hmax = displacement  = S = 80 m

• Hence at maximum height, the velocity of a ball becomes zero.

        i.e. final velocity v = 0 m/s

• First, we have to find the initial velocity with which a ball is thrown upward.  

• By the kinematical law of equation

$v^2 = u^2$ + 2as

0 = $u^2$ + 2 (-9.81) (80)

• After solving above equation,

u = 39.6181 m/s

• The kinetic energy of ball is calculated as:

K.E = 0.5 × m$u^2$

     = 0.5 × 0.040 × 39.6181 (39.6181)

K.E = 31.3918 J

• Now, 40% of K.E = 0.40 × 31.3918 = 12.5567 J

12.5567 = 0.5 × m$v^2$

⇒ v = 25.05 m/s

• from the law of the kinematical equation, we can find the height

$v^2 = u^2$ + 2as

(25.05)(25.05) = (39.6181)(39.6181) + 2(-9.81) s

s = 48.01 m

Hence at a height of 48.01 m, the kinetic energy reduced by 40% of a ball.