Downward Projectile Motion on an Inclined Plane

[dakota224]

Homework Statement

A skateboarder in a death-defying stunt decides to launch herself from a ramp on a hill. The skateboarder leaves the ramp at a height of 1.4 m above the slope, traveling 15 m/s and at an angle of 40° to the horizontal. The slope is inclined at 45° to the horizontal. With what velocity does the skateboarder land on the slope?

Homework Equations

tanФ = -y/x
x=x₀+v₀cosθt
y=y₀+v₀sinθt-(1/2)gt₂

The Attempt at a Solution

I am really not sure how to go about this, especially how to incorporate the height of the ramp. I have not found any sample problems like this one, as they all seem to have the object shooting up the hill from flat ground rather than shooting down off a ramp, or similar ski jump problems do not account for ramp height. In addition, I'm not sure how to find a final velocity at the end - won't I have two components of velocity?

 

[dakota224]

Homework Statement

A skateboarder in a death-defying stunt decides to launch herself from a ramp on a hill. The skateboarder leaves the ramp at a height of 1.4 m above the slope, traveling 15 m/s and at an angle of 40° to the horizontal. The slope is inclined at 45° to the horizontal. With what velocity does the skateboarder land on the slope?

View attachment 97142

Homework Equations

tanФ = -y/x
x=x₀+v₀cosθt
y=y₀+v₀sinθt-(1/2)gt₂

The Attempt at a Solution

View attachment 97143
I am really not sure how to go about this, especially how to incorporate the height of the ramp. I have not found any sample problems like this one, as they all seem to have the object shooting up the hill from flat ground rather than shooting down off a ramp, or similar ski jump problems do not account for ramp height. In addition, I'm not sure how to find a final velocity at the end - won't I have two components of velocity?

I notice that I plugged in 14º and not 40º for the ramp angle right off the bat, but the answer would still be incorrect.

 

[gneill]

See if you can't turn it into a problem of an intersection of two functions. The typical equations of motion for projectile motion, where the x and y components are treated as separate functions of time, are just the equation of the trajectory in parametric form (the "parameter" being time t).

If you can write the trajectory in the form y(x) = <some function of x>, and the equation of the slope in the same fashion, then you should be able to find their points of intersection.