Question

when a ball is thrown vertically upwards it goes through a distance of 19.6m.find the initial velocity of the ball and the time taken by it to rise to the highest point.(acceleration due to gravity, & g =9.8m/s^2​

Answer 1

Question : -

When a ball is thrown vertically upwards it travels a distance of 19.6 meters . Find the initial velocity of the ball and the time taken by it to reach the highest point. ( take acceleration due to gravity ( g ) = - 9.8 m/s² )

Answer : -

Given : -

When a ball is thrown vertically upwards it travels a distance of 19.6 meters .

Required to find : -

• Initial velocity ?

• Time taken to reach the highest point ?

Equations used : -

v² - u² = 2as

v = u + at

Solution : -

When a ball is thrown vertically upwards it travels a distance of 19.6 meters .

So,

From the given information we can conclude that ;

• Final velocity of the ball ( v ) = 0 m/s

• Distance traveled ( s ) = 19.6 meters

Since,

The acceleration due to gravity will be acting .

However,

The ball ia moving against the acceleration due to gravity . So, we need to take the value of acceleration due to gravity in terms of negative .

• Acceleration due to gravity ( g ) = - 9.8 m/s

Now,

Let's find the value of Initial velocity .

Using the equation of motion ;

i.e. v² - u² = 2as

=> ( 0 )² - u² = 2 x - 9.8 x 19.6

=> 0 - u² = 2 x - 9.8 x 19.6

=> - u² = - 19.6 x 19.6

=> - u² = - 384.16

=> - ( u )² = - ( 384.16 )

=> u² = 384.16

=> u = √384.16

=> u = + 19.6 or - 19.6 meters

Since,

Initial velocity can't be in negative !

Hence,

• Initial velocity of the ball ( u ) = 19.6 meters

Now,

Let's find the time taken to reach the maximum height .

Using the equation of motion ,

i.e. v = u + at

This implies ;

=> 0 = 19.6 + ( - 9.8 ) ( t )

=> - 19.6 = - 9.8t

Taking - ( minus ) common

=> - ( 19.6 ) = - ( 9.8t )

Minus ( - ) get's cancelled on both sides

=> 19.6 = 9.8t

=> 9.8t = 19.6

=> t = 19.6/9.8

=> t = 2 seconds

Hence,

• Time taken ( t ) = 2 seconds

Therefore,

Initial velocity of the ball ( u ) = 19.6 meters

Time taken by the ball to reach the maximum height ( t ) = 2 seconds

Answer 2

$\mathcal{\huge{\fbox{\red{Question\:?}}}}$

✴ When a ball is thrown vertically upwards it goes through a distance of 19.6m.find the initial velocity of the ball and the time taken by it to rise to the highest point.(acceleration due to gravity, & g =9.8m/s².

$\mathcal{\huge{\fbox{\green{Answer:-}}}}$

✏ The initial velocity of the ball ( u ) = 19.6 meters & the time taken by it to rise to the highest point is 2 second.

$\mathcal{\huge{\fbox{\purple{Solution:-}}}}$

⚽ Given :-

• The vertically upwards distance of the ball = 19.6 meters .

✨ To find :-

• The initial velocity of the ball.

• The time taken by it to rise to the highest point.

⭐ Calculation :-

According to the question,

Here, the ball is thrown vertically upwards it travels a distance of 19.6 meters .

• The ball is thrown vertically upwards .So, The final velocity of the ball ( v ) = 0 m/s

• Distance traveled by the ball is ( s ) = 19.6 meters

The ball is moving vertically upwards against the gravity to gravity.

So our acceleration is -ve. .

Therefore, our acceleration due to gravity ( g ) =

- 9.8 m/s.

Using 3rd equation of motion.

◼ v² - u² = 2as

Using given data,

➡ ( 0 )² - u² = 2 x - 9.8 x 19.6

➡ 0 - u² = 2 x - 9.8 x 19.6

➡ - u² = - 19.6 x 19.6

➡ - u² = - 384.16

➡ - ( u )² = - ( 384.16 )

➡ u² = 384.16

➡ u = √384.16

➡ u = ± 19.6 m

Hence, Initial velocity of the ball ( u ) = 19.6 meters.

Now, finding the time taken to reach the maximum height .

Using the first equation of motion ,

◼ v = u + at

Using given data,

➡ 0 = 19.6 + - 9.8 . t

➡ - 19.6 = - 9.8t

➡ 19.6 = 9.8t

➡ t = 19.6/9.8

➡ t = 2 seconds

Hence, the time taken is 2 seconds.

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