question about EK1001 physics

[visionboy]

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Ignoring air resistance, if the initial height of a body in
free fa ll is increased by a factor of 4, the final velocity
when it hits the ground will increase by a factor of:

A. 2
B. 4
C. It depends upon the value of the initial heigh t.
D. The velocity will remain the same.

Please help and provide with explanation. Thanks

 

[theonlytycrane]

potential energy (mgh) is being converted to kinetic energy (1/2 * m * v^2). Setting these two equal: v = sqrt(2 * g * h).

If h increases by a factor of 4, v increases by a factor of 2.