Question

When the skater starts 7 above the ground, how does the speed of the skater at the bottom of the track compare to the speed of the skater at the bottom when the skater starts 4 above the ground?

A. twice as fast.
B. higher, but less than twice as fast.
C. the same.
D. four times as fast.

Answer 1

A. twice as fast.

Step-by-step explanation:

m = Mass of skater

h = Height from where the skater starts

g = Acceleration due to gravity = 9.81 m/s²

Here the kinetic and potential energies balance each other

`K=P\\\Rightarrow (1)/(2)mv^2=mgh\\\Rightarrow v=√(2gh)`

Velocity from 7 m

`v_1=√(2g7)`

Velocity from 4 m

`v_2=√(2g4)`

Dividing the two equations

`(v_1)/(v_2)=(√(2g7))/(√(2g4))\\\Rightarrow (v_1)/(v_2)=1.32\approx 2\\\Rightarrow v_1\approx 2v_2`

So, the velocity of the skater is twice as fast