Downward Projectile Motion on an Inclined Plane

In summary, the problem involves a skateboarder launching off a ramp on a hill with an initial velocity of 15 m/s at an angle of 40° to the horizontal. The ramp is inclined at 45° to the horizontal and the skateboarder lands on the slope. The solution involves finding the intersection of the trajectory and slope equations, which can be written in parametric form as functions of time.
  • #1
dakota224
19
1

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?

skateboard.png


Homework Equations


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

The Attempt at a Solution


BD33A846-E142-4B4E-B293-E051532A0C82.JPG

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?
 
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  • #2
dakota224 said:

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.
 
  • #3
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.
 

1. What is downward projectile motion on an inclined plane?

Downward projectile motion on an inclined plane refers to the movement of an object that is launched or dropped from a higher point on an inclined plane and moves downward due to the force of gravity.

2. How does the angle of the incline affect the motion of the object?

The angle of the incline affects the motion of the object by changing the acceleration due to gravity. The steeper the angle, the greater the acceleration and therefore the faster the object will move down the incline.

3. What is the equation for calculating the speed of an object in downward projectile motion on an inclined plane?

The equation for calculating the speed of an object in downward projectile motion on an inclined plane is v = √(2ghsinθ), where v is the speed, g is the acceleration due to gravity, h is the height of the incline, and θ is the angle of the incline.

4. How does friction affect the motion of the object on an inclined plane?

Friction can slow down the motion of the object on an inclined plane, as it acts against the direction of motion. The amount of friction depends on the surface of the incline and the mass and speed of the object.

5. What factors can affect the distance traveled by an object in downward projectile motion on an inclined plane?

The distance traveled by an object in downward projectile motion on an inclined plane can be affected by the angle of the incline, the initial speed of the object, the mass of the object, and the presence of friction. Other factors such as air resistance and wind can also play a role.

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