A small circular object with mass m and radius r has a moment of inertia given by

I = cmr2.
The object rolls without slipping along the track shown in the figure. The track ends with a ramp of height R = 3.0 m that launches the object vertically. The object starts from a height H = 9.0 m. To what maximum height will it rise after leaving the ramp if c = 0.39?

I am really confused about this, please help thanks!

The figure is necessary

There is a table on top there is a string attached to a pulley and than a block is hanged down,which is also attached to the string!

Sorry ignore what I said here before...the ball is at the top and it slides to the right then it goes up a little which makes a curve which is distance R and the distance it slides from top to botton is H...hope you have an idea now!

To Priyanka ???

To find the maximum height the object will reach after leaving the ramp, we need to consider the conservation of mechanical energy.

1. Start by calculating the initial kinetic energy (KE) of the object:
The object is rolling without slipping, so its kinetic energy is a combination of the translational and rotational kinetic energies.

The translational kinetic energy is given by:
KE_translational = (1/2) * m * v^2

The rotational kinetic energy is given by:
KE_rotational = (1/2) * I * ω^2

Since the object is rolling without slipping, the velocity (v) and angular velocity (ω) are related:
v = ω * r

Substituting the expression for ω into the rotational kinetic energy equation:
KE_rotational = (1/2) * I * (v^2 / r^2) = (1/2) * I * (ω^2 * r^2 / r^2) = (1/2) * I * ω^2

Combining the translational and rotational kinetic energies:
KE = KE_translational + KE_rotational = (1/2) * m * v^2 + (1/2) * I * ω^2

2. Next, calculate the initial potential energy (PE) of the object:
PE = m * g * H

Where m is the mass of the object, g is the acceleration due to gravity, and H is the initial height.

3. The total mechanical energy (E) of the system is conserved throughout the motion:
E = KE + PE

Since the object starts from rest at the top, its initial kinetic energy is zero:
E = PE

4. Now, calculate the final potential energy (PE_f) when the object reaches the maximum height after leaving the ramp:
PE_f = m * g * h_f

Where h_f is the maximum height reached after leaving the ramp.

5. Set the initial potential energy equal to the final potential energy:
PE = PE_f

m * g * H = m * g * h_f

Canceling out the mass and the acceleration due to gravity, the equation becomes:
H = h_f

So the maximum height the object will reach after leaving the ramp is equal to the initial height, which is 9.0 m.

Therefore, the object will rise to a maximum height of 9.0 m after leaving the ramp.