VCAA Physics How do physicists explain motion in two dimensions?

This is correct. The net force is the component of gravity down the slope ($mg \sin 35^\circ \approx 112.4\text{ N}$) minus the opposing frictional force ($40\text{ N}$), resulting in a net force of $72.4\text{ N}$. Dividing by the mass ($20\text{ kg}$) gives $a \approx 3.6\text{ m s}^{-2}$.

This answer ignores the frictional force. It calculates the acceleration based solely on the component of gravity acting down the slope ($a = g \sin 35^\circ \approx 5.6\text{ m s}^{-2}$).

This calculation incorrectly uses the cosine function for the parallel component of gravity ($mg \cos 35^\circ$) instead of the sine function. The cosine component represents the normal force, not the force pulling the object down the slope.

This result incorrectly adds the frictional force to the gravitational component instead of subtracting it. Friction always opposes the direction of motion, so it must be subtracted from the driving force.

This is the initial vertical velocity, calculated using $v_y = v \sin(\theta) = 38 \sin(42^\circ) \approx 25 \text{ m s}^{-1}$.

The horizontal component of velocity is found using the cosine of the angle: $v_x = v \cos(\theta) = 38 \cos(42^\circ) \approx 28.2 \text{ m s}^{-1}$.

This value is incorrect; it does not result from applying the trigonometric component formulas to the given velocity and angle.

This is impossible because a component of the velocity vector ($v_x$) cannot be greater than the total magnitude of the velocity ($38 \text{ m s}^{-1}$).