Question

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Answer 1

Given :

➳ Mass of ball = 250g

➳ Initial velocity = 120kmph

➳ Final velocity = 60kmph

➳ The time of impact = 0.1s

To Find :

⟶ Force exerted on the ball.

Solution :

➠ This question is completely based on the newton's second law of motion.

➠ As per this law, Force is defined as the rate of change of linear momentum.

$\bigstar\:\boxed{\bf{F=\dfrac{dP}{dt}}}$

➠ Momentum is defined as the product of mass and velocity.

$\bigstar\:\boxed{\bf{F=\dfrac{m(v-u)}{dt}}}$

Where,

◕ F denotes force

◕ m denotes mass

◕ v denotes final velocity

◕ u denotes initial velocity

◕ t denotes time

✴ Conversion :

⟹ 1km/h = 5/18m/s

⟹ 120km/h = 120×5/18 = 33.33m/s

⟹ 60km/h = 60×5/18 = 16.67m/s

⟹ 250g = 250/1000 = 0.25kg

✴ Calculation :

$\longrightarrow\tt\:F=\dfrac{m(v-u)}{dt}\\ \\ \longrightarrow\tt\:F=\dfrac{0.25[33.33-(-16.67)]}{0.1}\\ \\ \longrightarrow\tt\:F=\dfrac{0.25\times 50}{0.1}\\ \\ \longrightarrow\boxed{\bf{F=125\:N}}$

[Note : -ve sign of u denotes opposite direction.]

Answer 2

mass of the ball( m) = 250 g = 0.25 kg

speed of the ball = 120 km hr

( in order to convert it into m / s multiply by 5/18 )

speed of the ball

= 120 ×5 / 18

= 33.3 m / s

speed of the ball ( v 1) = 33.3 m / s

time of impact of ball (t )= 0.1 sec

After striking the ball bounces back with half it's speed

i.e 33.3 / 2 = - 16.65 m / s

( - ve sign denotes that the ball is moving in opposite direction )

v 2 = - 16 . 65 m / s

We need to find the force (F) exerted on the ball,

We know that ,

$F = \frac{ \Delta \: P}{t}$

$F = \frac{ mv1 - mv2}{t}$

$F = \frac{ m(v1 - v2)}{t}$

$F = \frac{ 0.25(33.3 + 16.65)}{0.1}$

$F = \frac{0.25 \times 49.95}{0.1}$

$\boxed{F = 124.8N}$