Question

You are designing a ski jump ramp for the next Winter Olympics. Youneed to calculate the vertical height from the starting gate to the bottom of the ramp. Theskiers push off hard with their ski poles at the start, just abovethe starting gate, so they typically have a speed of 2.0 as they reach the gate. For safety, the skiersshould have a speed of no more than 30.0 when they reach the bottom of the ramp. Youdetermine that for a 86.0 skier with good form, friction and air resistance will dototal work of magnitude 4000 on him during his run down the slope.What is themaximum height for which the maximum safe speed will not be exceeded?

Answer 1

50.41 m

Step-by-step explanation:

From the law of conservation of energy

`KE_(1)+PE_(1)=KE_(2)+PE_(2)+W`

Where
`KE_(1),KE_(2),PE_(1),PE_(2)` are initial and final kinetic and potential energy respectively, W is Work.

Noting that final potential energy is zero then

`KE_(1)+PE_(1)=KE_(2)+W`

Since
`KE=0.5mv^(2)` where m is mass and v is velocity

PE=mgh where g is gravitational constant, h is height

`0.5mv_(1)^(2)+mgh=0.5mv_(2)^(2)+W`

Substituting m for 86Kg,
`v_(1)` for
`2m/s^(2)`, g for 9.81 m/s,
`v_(2)` for 30 m/s and W for 4000J

`0.5*86Kg*(2 m/s)^(2)+86Kg*9.81 m/s*h=0.5*86Kg*(30 m/s)^(2)+4000J`

172+843.66h=38700+4000

843.66h=42528

h=42528/843.66=50.40893

h=50.41 m