Question

A cricket ball is dropped from a height of 20 m. Calculate the speed of the Ball when it hits the ground and calculate the time it takes to fall through this height​

Answer 1

Here ,Initial speed u=0

Final speed v=? (to be calculated )

Acceleration due to gravity $g= 10\frac{m}{s^{2} }$   (Ball comes down)

height h=20 m

Now we know that for a freely falling body

$v^{2} =u^{2} +2gh\\v^{2} =(0)^{2} *10*20\\v^{2} =400\\v =\sqrt{400} \\v=\frac{m}{s}$

Thus the speed of cricket ball when it hits the ground will be 20 meters per second

Final speed v=20 m/s (calculated above )

Acceleration due to gravity $g=10\frac{m}{s^{2} }$ And Time,t =? (to be calculate

Putting these values in the formula :

we v=u+gt

$20=0+10*t\\10t=20\\t=\frac{20}{10} \\t=2$

Thus the ball takes 2 second to fall through a height of 20 metres .

Answer 2

Answer:

Given :-

• A cricket ball is dropped from a height of 20 m.

To Find :-

• What is the speed of the ball when it hits the ground.
• What is the time taken to fall through this height.

Formula Used :-

$\clubsuit$ Third Equation Of Motion Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{v^2 =\: u^2 + 2gh}}}\: \: \: \bigstar$

where,

• v = Final Velocity
• u = Initial Velocity
• g = Acceleration due to gravity
• h = Height

$\clubsuit$ First Equation Of Motion Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{v =\: u + gt}}}\: \: \: \bigstar$

where,

• v = Final Velocity
• u = Initial Velocity
• g = Acceleration due to gravity
• t = Time Taken

Solution :-

❒ First, we have to find the speed of the ball when it hits the ground :

Given :

• Initial Velocity (u) = 0 m/s
• Acceleration due to gravity (g) = 9.8 m/s²
• Height = 20 m

According to the question by using the formula we get,

$\implies \bf v^2 =\: u^2 + 2gh$

$\implies \sf v^2 =\: (0)^2 + 2(9.8)(20)$

$\implies \sf v^2 =\: (0 \times 0) + 2 \times 9.8 \times 20$

$\implies \sf v^2 =\: 0 + 19.6 \times 20$

$\implies \sf v^2 =\: 0 + 392$

$\implies \sf v^2 =\: 392$

$\implies \sf v =\: \sqrt{392}$

$\implies \sf v =\: 19.79$

$\implies \sf v \approx 20$

$\implies \sf\bold{\purple{v =\: 20\: m/s}}$

$\therefore$ The speed of the ball when it hits the ground is 20 m/s .

❒ Now, we have to find the time taken to fall through this height :

Given :

• Final Velocity (v) = 20 m/s
• Initial Velocity (u) = 0 m/s
• Acceleration due to gravity (g) = 9.8 m/s²

According to the question by using the formula we get,

$\implies \bf v =\: u + gt$

$\implies \sf 20 =\: 0 + 9.8t$

$\implies \sf 20 - 0 =\: 9.8t$

$\implies \sf 20 =\: 9.8t$

$\implies \sf \dfrac{20}{9.8} =\: t$

$\implies \sf 2.04 =\: t$

$\implies \sf 2 \approx t$

$\implies \sf\bold{\red{t =\: 2\: seconds}}$

$\therefore$ The time taken to fall through this height is 2 seconds .

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