Calculating Minimum Speed for a Successful River Jump

[DannyDon]

Homework Statement

A stunt motorcyclist has to jump across a river 7.0 m wide from a ramp on one side with incline of 10 degrees. (a) What minimum speed the motorcycle must have to successfully land on the opposite side of the river? (b) How long will the motorcyclist be in the air? (Assume equal elevation on the both sides of the river, ignore air resistance)

The Attempt at a Solution

I have no idea how to go about this, I've tried going through all of the kinematic equations with the 2 variables given. I'm assuming the extra information given after part (b) also relates to part (a) otherwise it would be impossible to solve? So my understanding is that there are 2 ramps on either side of the river, both of which have an incline of 10 degrees or am I misinterpreting the question?

 

[Ray Vickson]

Homework Statement

A stunt motorcyclist has to jump across a river 7.0 m wide from a ramp on one side with incline of 10 degrees. (a) What minimum speed the motorcycle must have to successfully land on the opposite side of the river? (b) How long will the motorcyclist be in the air? (Assume equal elevation on the both sides of the river, ignore air resistance)

The Attempt at a Solution

I have no idea how to go about this, I've tried going through all of the kinematic equations with the 2 variables given. I'm assuming the extra information given after part (b) also relates to part (a) otherwise it would be impossible to solve? So my understanding is that there are 2 ramps on either side of the river, both of which have an incline of 10 degrees or am I misinterpreting the question?

PF rules require that you show your work; saying you have no idea how to go about this is not considered to be a solution attempt.

 

[Delta2]

What equations are there in your book/notes about projectile motion with initial angle θ relative to the horizontal? Specifically look for the equations of the horizontal and vertical displacement (distance).

From the description of the problem we can't be sure about the existence of the 2nd ramp. Is there a figure/scheme that accompanies this problem? In my opinion I don't think that the existence of the 2nd ramp is implied by the other data of the problem.

 

[CWatters]

I think some assumptions are required. For example if the ramp was several hundred feet long the take off point would be quite high in relation to a landing point with no ramp. That would effect the minimum speed needed.

I think the angle of the ramp is only intended to give you the take off angle. So I would treat it as a simple projectile motion problem from ground level to ground level.

 

[haruspex]

So my understanding is that there are 2 ramps on either side of the river, both of which have an incline of 10 degrees

As others have written, you are probably supposed to assume take off and landing are at the same height, so, yes, you can treat it as two identical ramps.

 

[Delta2]

As others have written, you are probably supposed to assume take off and landing are at the same height, so, yes, you can treat it as two identical ramps.

I initially thought that this point was the "mini-trap" of this assignment, but then I saw that there is not enough data given to calculate the height from the launch ramp, so either the OP forgot to tell us some additional data (like for example what is the horizontal length of the ramp) or we ll have to assume as you say.