Question

If the ratio of the final velocities of two bodies falling freely is 4:3,then the ratio of the heights from which they fall is?

Answer 1

Let the two bodies fall from heights H and h, such that H>h. Now for a body dropped from height H and falling freely itsvelocity V on reaching the ground is

V²= 2 g H,……..1

For the body dropped from height h and falling freely, its velocity v, on reaching the ground is,

v² = 2 g h,

Now V/v = 4/3, (given)or V²/v² = 16/9,

Now

H/h = V²/v² = 16/9.

**as height is just the square of the given final velocity

source :qoura

Answer 2

Let the two bodies fall from heights H and h, such that H>h. Now for a body dropped from height H and falling freely itsvelocity V on reaching the ground is

V²= 2 g H,……..1

For the body dropped from height h and falling freely, its velocity v, on reaching the ground is,

v² = 2 g h,

Now V/v = 4/3, (given)or V²/v² = 16/9,

Now

H/h = V²/v² = 16/9.

Therefore the two heights are in the ratio of 16:9.

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