A ball starts from rest down a smooth (frictionless) 45 degree inclined plane 10 m above the floor. How fast will it be going when it reaches the floor?

a solid ball, or hollow?

is it rolling? Without friction, it wont roll.

So I don't know enough to answer you?

just a ball (nothing else is given for this ball) the ball is at rest 10 m above the horizontal on a 45 degree smooth inclined plane. Vi= 0 m/s, height = 10 m, Vf =?

To find the speed of the ball when it reaches the floor, we can use the principles of conservation of mechanical energy and the concept of gravitational potential energy.

1. First, let's calculate the potential energy of the ball when it is at the top of the incline. The potential energy (PE) is given by the equation PE = m * g * h, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height (10 m).

2. Next, we can calculate the angle of the incline, which is given as 45 degrees. We can use this angle to find the component of the gravitational force acting on the ball along the incline. The component of the gravitational force (mg) along the incline is given by mg * sin(θ), where θ is the angle of the incline.

3. Now, we can find the work done by the gravitational force on the ball as it moves down the incline. The work done (W) is equal to the change in gravitational potential energy, which is given by W = PE_final - PE_initial.

4. Since the ball starts from rest, its initial kinetic energy (KE_initial) is zero. Therefore, the work done by the gravitational force is equal to the initial kinetic energy of the ball just before it reaches the floor (KE_final).

5. We can use the equation KE = (1/2) * m * v^2, where v is the final velocity of the ball at the bottom of the incline.

6. Equating the work done by the gravitational force to the kinetic energy, we have:
mg * sin(θ) * d = (1/2) * m * v^2
Here, d is the distance traveled by the ball on the incline. In this case, it is the same as the height (10 m).

7. Simplifying the equation, we have:
g * sin(θ) * d = (1/2) * v^2

8. Rearranging and solving for v, we get:
v = √(2 * g * sin(θ) * d)

Now, we can substitute the known values: g = 9.8 m/s^2, θ = 45 degrees, and d = 10 m to find the final velocity (v) of the ball when it reaches the floor.