Minimum Speed for Motorcyclist to Successfully Cross a Ravine

In summary: I'll leave it to you to finish off the details.In summary, the task is to calculate the minimum speed a motorcyclist must have when leaving a ramp at a 40 degree angle to successfully cross a 10.0 meter wide ravine that is 2.0 meters higher on the far side. By equating the x and y equations and using the known values for acceleration, initial position, and final position, it is possible to solve for the initial velocity needed, which was found to be 9.92m/s. However, this value may not be sufficient to clear the ravine and therefore further calculations may be necessary.
  • #1
ladymiresa
4
0

Homework Statement


A motorcyclist must cross a ravine. The far side of the ravine is 2.0 meters higher than the launch point, a ramp that makes an angle of 40◦ with the horizontal. If the ravine is 10.0 meters wide, what minimum speed v must the biker have when leaving the ramp to successfully cross the ravine? Take the launch point at the end of the ramp as the coordinate origin.

Homework Equations


yf=yi+(vi)t-.5g(t^2)

The Attempt at a Solution



Well, I know that Vxi=vicos40 and vyi=visin40.
Known: xi=0, yi=0, ti=0, xf=10, yf=2, theta=40, ay=-9.8
I want to use to equation above, but I can't because I know neither the Vi nor the T. I thought I could figure out the T by saying that the initial vy was zero, but that definitely doesn't seem right because then only gravity would be acting on the bike and he has to GAIN 2m in height. So I'm a little stuck. I'd really appreciate any tips to help me figure out this problem!
 
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  • #2
You have two equations, one in the y direction and one in the x direction. There are two unknowns they share.
 
  • #3
The only equation in the x direction I can think of is xf=xi+(vx)i*t, and here I still have two unknowns (xfi and t).
 
  • #4
ladymiresa said:
The only equation in the x direction I can think of is xf=xi+(vx)i*t, and here I still have two unknowns (xfi and t).
No, the two unknowns there are vx and t, surely? And you can express vx in terms of v and theta. So as I posted, both unknowns appear in both equations. Two equations, two unknowns.
 
  • #5
Ah, yes, I definitely meant Vx and t for the unknowns.

So, if I say that vx=vicos40 then I can rewrite the equation as xf=xi+(vicos40)t... which can be rearranged to say t=xf]-xi/(vicos40).

then I think I can substitute into the first equation:
yf=yi+(visin40)(xf-xi/vicos40)+.5(-9.8)(xf-xi/vicos40)^2. So my only unkown is vi! ...Now, if only I can get the math right haha..

Ok, I calculated that Vi=9.92m/s. I think this makes sense. Thanks for helping me, I never would have thought to substitute the equations on my own.
 
  • #6
ladymiresa said:
Ah, yes, I definitely meant Vx and t for the unknowns.

So, if I say that vx=vicos40 then I can rewrite the equation as xf=xi+(vicos40)t... which can be rearranged to say t=xf]-xi/(vicos40).

then I think I can substitute into the first equation:
yf=yi+(visin40)(xf-xi/vicos40)+.5(-9.8)(xf-xi/vicos40)^2. So my only unkown is vi! ...Now, if only I can get the math right haha..

Ok, I calculated that Vi=9.92m/s. I think this makes sense. Thanks for helping me, I never would have thought to substitute the equations on my own.

9.92m/s isn't fast enough. You'll end up in the ravine at that speed! Maybe check the maths.
 
  • #7
ladymiresa said:
Ah, yes, I definitely meant Vx and t for the unknowns.

So, if I say that vx=vicos40 then I can rewrite the equation as xf=xi+(vicos40)t... which can be rearranged to say t=xf]-xi/(vicos40).

then I think I can substitute into the first equation:
yf=yi+(visin40)(xf-xi/vicos40)+.5(-9.8)(xf-xi/vicos40)^2. So my only unkown is vi! ...Now, if only I can get the math right haha..

Ok, I calculated that Vi=9.92m/s. I think this makes sense. Thanks for helping me, I never would have thought to substitute the equations on my own.
I haven't checked your arithmetic, but good to see that you get the method.
 

Related to Minimum Speed for Motorcyclist to Successfully Cross a Ravine

What is the minimum speed required to cross a ravine?

The minimum speed required to cross a ravine depends on various factors such as the width and depth of the ravine, the weight of the person crossing, and the slope of the terrain. In general, a minimum speed of 10-15 miles per hour is recommended to safely cross a ravine.

What happens if I don't reach the minimum speed while crossing a ravine?

If you do not reach the minimum speed while crossing a ravine, you may not have enough momentum to successfully make it to the other side. This can result in falling into the ravine and potentially causing serious injuries or even death.

Can I use a vehicle to cross a ravine at a minimum speed?

Yes, you can use a vehicle to cross a ravine at a minimum speed as long as the vehicle is properly equipped and able to maintain a steady speed. It is important to carefully assess the conditions of the ravine and terrain before attempting to cross with a vehicle.

How can I calculate the minimum speed needed to cross a ravine?

To calculate the minimum speed needed to cross a ravine, you will need to consider the various factors such as the width and depth of the ravine, the weight of the person or vehicle crossing, and the slope of the terrain. You can use physics equations and formulas to determine the minimum speed required.

What precautions should I take when attempting to cross a ravine at minimum speed?

When attempting to cross a ravine at minimum speed, it is important to take necessary precautions such as wearing appropriate safety gear, assessing the terrain and conditions beforehand, and having a backup plan in case of any emergencies. It is also recommended to have an experienced guide or professional accompany you for added safety.

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