Find Distance Block Falls from Table Edge: Forces on an Incline

[tyro008]

Question:
A block of mass m = 2.00 kg is released from rest at h = 0.600 m from the surface of a table, at the top of a θ = 35.0° incline as shown below. The frictionless incline is fixed on a table of height H = 2.00 m.
How far from the table will the block hit the floor?

So basically a block falls from a ramp on top of a table and I'm supposed to figure out how far the block falls from the edge of the ramp (which is on the edge of the table).
I would use a kinematics equation but I have another unknown besides the distance.
I figured out the final velocity at the edge of the ramp and the length of the hypotenuse of the ramp and the acceleration during the ramp time but I don't know anything about the ramp time.

 

[Hootenanny]

Question:
A block of mass m = 2.00 kg is released from rest at h = 0.600 m from the surface of a table, at the top of a θ = 35.0° incline as shown below. The frictionless incline is fixed on a table of height H = 2.00 m.
How far from the table will the block hit the floor?

So basically a block falls from a ramp on top of a table and I'm supposed to figure out how far the block falls from the edge of the ramp (which is on the edge of the table).
I would use a kinematics equation but I have another unknown besides the distance.
I figured out the final velocity at the edge of the ramp and the length of the hypotenuse of the ramp and the acceleration during the ramp time but I don't know anything about the ramp time.

Welcome to PF tyro008,

You made a good start by determining the velocity of the block at the point of leaving the ramp. Now try splitting the velocity of the block into vertical and horizontal components and see what you can do from there.

 

[baba89]

I would approach this problem by using the principles of mechanics and kinematics to solve for the unknown variables. First, I would draw a free-body diagram of the block on the incline to identify all the forces acting on it. These forces would include the weight of the block, the normal force from the incline, and the force of gravity acting on the block.

Next, I would use the equations of motion to analyze the motion of the block. Since the block starts from rest, we can use the equation vf^2 = vi^2 + 2ad to solve for the final velocity at the edge of the ramp. The initial velocity, vi, is 0 m/s and the acceleration, a, can be calculated using the angle of the incline and the gravitational acceleration (9.8 m/s^2).

Once we have the final velocity, we can use the equation d = vit + 1/2at^2 to solve for the distance the block travels before hitting the floor. The initial time, ti, is also 0 seconds and the final time, tf, is what we are trying to solve for. We can use the equation vf = vi + at to solve for tf.

Finally, we can substitute the value of tf into the equation for distance to calculate the distance the block falls from the edge of the ramp. This will give us the distance from the edge of the ramp to the point where the block hits the floor.

In summary, by using the principles of mechanics and kinematics, we can solve for the distance the block falls from the edge of the ramp. It is important to carefully analyze the problem and identify all the forces and variables involved in order to accurately solve for the unknown.