Question

A marble is rolling across the floor at a speed of 7.0 m/s when it starts up a plane inclined at 30° 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?

(a) 14.5 m
(b) 17.3 m
(c) 20.1 m
(d) 23.0 m

Answer 1

The marble travels approximately 14.5 m along the inclined plane before coming to rest. It takes approximately 1.19 seconds for the marble to move up the plane.

Step-by-step explanation:

The distance along the plane that the marble travels before coming to rest can be calculated using the equation:

d = v2sin(2θ)/g

Where:

• d is the distance along the plane
• v is the initial velocity of the marble (7.0 m/s)
• θ is the angle of incline (30°)
• g is the acceleration due to gravity (9.8 m/s²)

Plugging in the values, we get:

d = (7.02)sin(2*30°)/9.8

d ≈ 14.5 m

The time it takes for the marble to move up the plane can be calculated using the equation:

t = v*sin(θ)/g

Where:

• t is the time
• v is the initial velocity of the marble (7.0 m/s)
• θ is the angle of incline (30°)
• g is the acceleration due to gravity (9.8 m/s²)

Plugging in the values, we get:

t = 7.0*sin(30°)/9.8

t ≈ 1.19 s