Physics 9702 · AS & A Level · Momentum and Newton's laws of motion

Momentum and Newton's laws of motion — practice question

A skier is dragged in a straight line across level ground by a wire attached to a kite. The skier has mass $89\,\text{kg}$. The wire makes an angle of $28^\circ$ with the horizontal. Fig. 2.2 shows how the skier’s velocity $v$ varies with time $t$.
(a)[1]

State Newton’s first law of motion in your own words.

(b(i))[2]

Use Fig. 2.2 to find how far the skier travels from time $t = 0$ to $t = 5.0\,\text{s}$.

(b(ii))[2]

Use Fig. 2.2 to demonstrate that the skier’s acceleration $a$ is $0.80\,\text{m s}^{-2}$ at time $t = 2.0\,\text{s}$.

(b(iii).1)[1]

The tension in the wire at time $t = 2.0\,\text{s}$ is $240\,\text{N}$. Calculate the horizontal part of the tension force acting on the skier.

(b(iii).2)[2]

Calculate the total resistive force $R$ that acts on the skier horizontally.

(b(iv))[2]

The skier is now lifted upwards by a gust of wind. For a few seconds the skier moves horizontally through the air with the wire at an angle of $45^\circ$ to the horizontal. By considering the vertical components of the forces acting on the skier, determine the new tension in the wire when the skier is moving horizontally through the air.

(ii)[2]

Use Fig. 2.2 to demonstrate that the skier’s acceleration $a$ is $0.80\,\text{m s}^{-2}$ at time $t = 2.0\,\text{s}$.

(iii.1)[1]

The tension in the wire at time $t = 2.0\,\text{s}$ is $240\,\text{N}$. Calculate the horizontal part of the tension force acting on the skier.

(iii.2)[2]

The tension in the wire at time $t = 2.0\,\text{s}$ is $240\,\text{N}$. Calculate the total resistive force $R$ acting on the skier in the horizontal direction.

(iv)[2]

The skier is now lifted upwards by a gust of wind. For a few seconds the skier moves horizontally through the air with the wire at an angle of $45^\circ$ to the horizontal, as shown in Fig. 2.3. By considering the vertical components of the forces acting on the skier, determine the new tension in the wire when the skier is moving horizontally through the air.

Worked solution & mark scheme

This 17-mark question has a full step-by-step worked solution and mark scheme. One marking point: A body stays at rest or moves with constant velocity unless a resultant force acts on it

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