Question

suppose you drop a ball from a certainheightand find itsfinal speedis 20 m/s when it hits the ground.if you throw the objectvertically downwards from the sameheight with an initial speed of 20 m/s, will its finalspeed be 40m/s? carefully explain why or why not (ignore friction)

Answer 1

In the case of free fall , initial speed of an object will be zero.

Initial speed of the ball be u = 0

Then final speed v ( speed of the ball when it hits the ground ) can be calculated when the height is given using the formula

v² = 2 g h

where g = 9.81 m/s² is the acceleration due to gravity

h is the height from which ball is falling.

Here final speed is given and we have to calculate the height.

Final speed v = 20 m/s

( 20 )² = 2 × 9.81 × h

400 = 19.62 h

h = 400 / 19.62

h = 20.38 m

So ball is released from a height h = 20.38 m

We can use this data to calculate the final speed of an object when it is thrown with an initial speed u' from the same height.

Initial speed of the ball u' = 20 m/s

Final speed v' is given by

v'² - u'² = 2 g h

v'² - ( 20 )² = 2 × 9.81 × 20.38

v'² - 400  = 400

v'² = 400 + 400

v'² = 800

v' =  800

v' = 28.28 m/s

When the ball is thrown downwards with an initial speed u' = 20 m/s , its final speed would be 28.28 m/s

It is not 40 m/s . Final speed does not linearly depend on height ( provided the g value is constant.) It depends on the square root of the height from which object is falling.

When an object is freely falling , final speed represents the change in speed of the object ( from 0 to a specific value )

Here final speed depends on root of the sum of square of initial speed and change in the speed.

It is not a direct sum of initial speed and change in the speed during the fall.

That's why we got the final speed of 28.28 m/s and not 40m/s.