Ski Ramp Physics: Find Initial Velocity & Injuries

[MarkGhent]

Homework Statement

A Skier leaves the ramp at 25 degrees inclined from the horizontal. The ramp is 4 meters above the ground. The skier lands 100 meters away. The ground itself is sloped from the ramp relating to a 3 4 5 triangle. I need to find the initial velocity off the ramp and the extent of the skiers injuires

Homework Equations

Range=(V^2/g)*sin2(theta)
Time of flight=(2V/g)sin(theta)
x=x(o) +V(o)T

The Attempt at a Solution

I used the range equation to find the initial velocity which i found to be 35.78m/s and then used that in the TOF equation to find the TOF to be 3.08s and then split the velocity into its horizontal and vertical components to get V(x)=32.42m/s V(y)=15.15m/s

I then used V(x) in the x=x(o)+V(o)t to get the x distance to make sure my numbers were right and i got X= 99.8m which is basically 100m. Am I going about this right or right and did the fact that a 3 4 5 triangle was drawn under the 100m distance matter at all?

 

[kamerling]

That equation for the range and time of flight is only valid for ballistic motion that returns to the same altitude. Since you start at 4m altitude and the ground is sloping away they aren't valid here.

you just have to guess a value of v for the initial velocity here. You can than get the time of flight from the distance and v_x. The time of flight and v_y will than give you the altitude at the end of the flight. If the end of the ramp has altitude 0, the ground will have an altitude of -4 - 3/4 x where x is the horizontal distance away from the ramp. (if I uncerstand your remark about a 3 4 5 triangle correctly.)