Question

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

Calculate

(a) the velocity of the ball with which it hits the ground

( b ) the time it takes to fall through this height. (g = 10

ms ^ 2)​

Answer 1

Given :-

A cricket ball is dropped from a height of 20 m

Required to find :-

• Velocity of the ball with which it hits the ground ?

• Time taken by it to fall through this height ?

Hint mentioned :-

Take g as 10 m/s²

Equation used :-

v² - u² = 2as

s = ut + ½ at²

Solution :-

Given data :-

A cricket ball is dropped from a height of 20 meters

we need to find the velocity of the ball with which it hits the ground and the time taken by it to fall through this height .

From the given information we can conclude that ;

• Initial velocity of the cricket ball ( u ) = 0 m/s

• Height ( s ) = 20 meters

• Acceleration due to gravity ( g ) = 10 m/s²

Using the equation of motion ;

v² - u² = 2as

v² - ( 0 )² = 2 x 10 x 20

v² - 0 = 2 x 200

v² = 400

v = √400

v = 20

Hence,

• Final velocity of the ball ( v ) = 20 m/s

Now,

Using the 2nd equation of motion ;

➤ s = ut + ½ at²

➤ 20 = 0 x t + ½ x 10 x t²

➤ 20 = 0 + ½ x 10 x t²

➤ 20 = 0 + 5 x t²

➤ 20 = 0 + 5t²

➤ 20 = 5t²

➤ 5t² - 20 = 0

➤ 5 ( t² - 4 ) = 0

➤ t² - 4 = 0/5

➤ t² - 4 = 0

➤ ( t )² - ( 2 )² = 0

➤ ( t + 2 ) ( t - 2 ) = 0

This implies,

=> t + 2 = 0

=> t = - 2

similarly,

=> t - 2 = 0

=> t = 2

Since, time can't be in negative

• Time taken by the ball ( t ) = 2 seconds

Therefore,

The velocity of the ball with which it hits the ground = 20 m/s

The time it takes to fall through this height = 2 seconds

Answer 2

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Explanation:

Here ,Initial speed u=0

Final speed v=? (to be calculated )

Acceleration due to gravity g=10m/s2 (Ball comes down)

height h=20 m

Now we know that for a freely falling body

v2=u2+2gh

v2=(0)2+×10×20

v2=400

v=400−−−√

v=m//s

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

(b ) Now , Initial speed u=0 n

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

Acceleration due to gravity g=10 m/s^2 And Time,t =? (to be calculated )

Putting these values in the formula :

we v=u+gt

20=0+10×t

10 t= 20 ltnrgt t=2010

t= 2 s

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