Question

question 15 (1 point)
suppose a can, after an initial kick, moves up along a smooth hill of ice. make a statement concerning its acceleration.
it will travel at constant velocity with zero acceleration.
it will have a constant acceleration up the hill, but a different constant acceleration when it comes back down the hill.
it will have the same acceleration, both up the hill and down the hill.
it will have a varying acceleration along the hill.

Explanation:

The can moves on a smooth (frictionless) ice hill. The only significant force acting along the hill is the component of gravity parallel to the hill's surface. Since the slope of the hill (angle) is constant, the component of gravity parallel to the hill ($F = mg\sin\theta$, where $m$ is mass, $g$ is gravitational acceleration, $\theta$ is the angle of the hill) is constant. By Newton's second law ($F = ma$), acceleration $a=\frac{F}{m}=g\sin\theta$, which is constant (same magnitude and direction, as the component of gravity parallel to the hill is always down the hill, causing deceleration when moving up and acceleration when moving down, but the magnitude of acceleration remains the same as $\theta$ and $g$ are constant). So the acceleration is the same (in magnitude and direction relative to the hill's axis) both up and down the hill.

• Option 1: Wrong, because there is a component of gravity causing acceleration (not zero velocity).
• Option 2: Wrong, acceleration magnitude (and direction relative to the hill's motion axis) is the same as the force component and mass don't change.
• Option 4: Wrong, acceleration is constant (since force and mass are constant), not varying.

Answer:

It will have the same acceleration, both up the hill and down the hill.