Question

a marble is rolling across the floor at a speed of 7.0 m/s when it starts up a plane inclined at to the horizontal. (a) how far along the plane does the marble travel before coming to a rest? (b) how much time elapses while the marble moves up the plane?cx

Answer 1

The marble travels a distance of 8.34 m along the inclined plane before coming to a rest. The time elapsed while the marble moves up the plane is 2.38 seconds.

Step-by-step explanation:

To solve this problem, we can use the equations of motion. First, let's find the distance along the inclined plane that the marble travels before coming to rest:

The initial velocity (v0) is 7.0 m/s and the acceleration (aCM) is -g*sin(30°).

Using the equation v2 = v02 + 2aCMx, where v is the final velocity, we can solve for x. Plugging in the values, we get:

v2 = (7.0 m/s)2 - 2(9.8 m/s2)(x)

Solving for x, we find that the marble travels a distance of 8.34 m along the inclined plane before coming to a rest.

To find the time elapsed while the marble moves up the plane, we can use the equation v = v0 + aCMt, where t is the time elapsed. Plugging in the values, we have:

0 = 7.0 m/s - 9.8 m/s2t

Solving for t, we find that t = 2.38 s.