A skier of mass 50 kg stands at point P at the top of the ski jump and moves from P to Q and takes off his jump at Q as shown in figure. If 50% of the change in the gravitational potential energy of the skier between points P and Q becomes the kinetic energy at Q, then the speed at which the skier arrives at Q is

Options

A. `10 ms^(-1)`
B. `20 ms^(-1)`
C. `30 ms^(-1)`
D. `40 ms^(-1)`

Answer

B

Explanation

Change in gravitational potential energy of the skier,
`E_(p)="mgh" = 50 xx 10 xx [60-20]`
`=20000J =2 xx 10^(4)J`
Kinetic energy, `E_(k) = 50%` of `E_(p)=(1)/(2) xx 2 xx 10^(4) J=1xx10^(4)J`
`E_(k)=(1)/(2)mv^(2) rArr v= sqrt((2E_(k))/(m))=sqrt((2xx1xx10^(4))/(50))=20 ms^(-1)`