Having trouble finding the horizontal velocity of the object rolling down a ramp

[yokialana]

Homework Statement

I need to find the horizontal velocity of an object on a ramp where the first height is 5.0m and the second height is 3.0m? I also need to find the time it takes to fall from the ramp, and the distance it falls away from the ramp. I am only given the two heights, an initial velocity of 0, and of course I have gravity.

Homework Equations

ep=mgh
ek=0.5mv2

The Attempt at a Solution

Not sure where to start even.

 

[PeterO]

Homework Statement

I need to find the horizontal velocity of an object on a ramp where the first height is 5.0m and the second height is 3.0m? I also need to find the time it takes to fall from the ramp, and the distance it falls away from the ramp. I am only given the two heights, an initial velocity of 0, and of course I have gravity.

Homework Equations

ep=mgh
ek=0.5mv2

The Attempt at a Solution

Not sure where to start even.

I can see your dilemma - I think you need the either the angle of, or the length of, the ramp.

It is fine to use energy considerations to calculate how fast the object [presumably sliding down a frictionless ramp] will be traveling when it leaves the lower end of the ramp, but without an angle you are stumped - other than to derive an answer which includes a variable like θ which could represent the angle of the ramp.

I assume frictionless, as any friction would complicate matters, and also assume sliding not rolling, as angular momentum/energy would otherwise affect the answer.

 

[yokialana]

Does anybody know if it would work to use the kinematic equation vf2 = vi2 +2ad? I have all the variables to solve for final velocity. But I'm not sutre if it's different because it applies to a curved ramp. Plus this is in the work/energy unit so i don't know why my teacher would want me using that. I'm uber confused. This would be so much easier if I had mass.

 

[PeterO]

Does anybody know if it would work to use the kinematic equation vf2 = vi2 +2ad? I have all the variables to solve for final velocity. But I'm not sutre if it's different because it applies to a curved ramp. Plus this is in the work/energy unit so i don't know why my teacher would want me using that. I'm uber confused. This would be so much easier if I had mass.

Are you saying this ramp is curved?

Does the object leave the ramp traveling horizontally?

You definitely don't need the mass of the object.

 

[Nickie]

As a scientist, it is important to approach problems systematically and use the appropriate equations and principles to solve them. In this case, we can use the principles of conservation of energy and kinematics to find the horizontal velocity, time of fall, and distance traveled.

First, we can use the conservation of energy principle to relate the potential energy at the first height (mgh1) to the kinetic energy at the second height (0.5mv^2). Since the initial velocity is 0, we can simplify the equation to mgh1 = 0.5mv^2.

Next, we can use the kinematic equation for motion with constant acceleration (in this case, due to gravity) to relate the initial height (5.0m), final height (3.0m), and time of fall (t). The equation is h = h0 + v0t + 0.5at^2, where h0 is the initial height, v0 is the initial velocity (which is 0 in this case), a is the acceleration due to gravity (9.8 m/s^2), and h is the final height. Rearranging this equation, we get t = √(2h/a).

Now, we can substitute this value of t into our first equation to solve for the horizontal velocity, v. This gives us v = √(2gh1).

Finally, to find the distance traveled away from the ramp, we can use the kinematic equation for motion with constant velocity (since the horizontal velocity remains constant throughout the motion). The equation is d = v0t + 0.5at^2, where d is the distance traveled, v0 is the initial velocity (0 in this case), a is the acceleration due to gravity (0 in the horizontal direction), and t is the time of fall that we calculated earlier.

Using these equations and principles, we can find the horizontal velocity, time of fall, and distance traveled for the object rolling down the ramp. It is important to always approach problems systematically and use the appropriate equations and principles to solve them.