A model rocket accelerates vertically upwards then decelerates due to gravity until it reaches a maximum height. (a) A velocity-time graph for the rocket until it reaches maximum height is shown. Velocity ms⁻¹ Show that the rocket reaches a maximum height of about 68 m. (b) When the rocket reaches the maximum height of 68 m, a parachute opens. Almost instantly, the rocket reaches a terminal velocity of 2.0 m/s. Complete the velocity-time graph below for the motion of the rocket until it reaches the ground. (c) The rocket is fired upwards a second time when the wind is blowing. The rocket falls with a vertical velocity of 2.0 m/s and a horizontal velocity of 1.5 m/s. Determine the velocity of the rocket by drawing a scaled vector diagram.

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A model rocket accelerates vertically upwards then decelerates due to gravity until it reaches a maximum height - Edexcel - A-Level Physics - Question 10 - 2023 - Paper 1

Question 10

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A model rocket accelerates vertically upwards then decelerates due to gravity until it reaches a maximum height. (a) A velocity-time graph for the rocket until it r... show full transcript

Worked Solution & Example Answer:A model rocket accelerates vertically upwards then decelerates due to gravity until it reaches a maximum height - Edexcel - A-Level Physics - Question 10 - 2023 - Paper 1

Step 1

Show that the rocket reaches a maximum height of about 68 m.

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Answer

To find the maximum height of the rocket, we need to calculate the area under the velocity-time graph.

The area under the graph between time 0 to 2 seconds (where the rocket is ascending) forms a triangle. The base of this triangle is the time interval of 2 seconds and the height is the maximum velocity of 30 m/s.

Using the formula for the area of a triangle:

$ext{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

we have:

$ext{Area} = \frac{1}{2} \times 2s \times 30 m/s = 30 m$

Next, for the time interval of 2 to 4 seconds (where the rocket is descending), the area forms a rectangle with a width of 2 seconds and a height of 30 m/s:

$ext{Area} = \text{width} \times \text{height} = 2s \times 30 m/s = 60 m$

Adding both areas together:

$30 m + 60 m = 90 m$

As gravitational deceleration affects the total height gained, we must use the net effect. Therefore, the total height is slightly less than this, and thus:

$ext{Maximum height} \approx 68 m.$

This confirms that the rocket reaches a maximum height of approximately 68 m.

Step 2

Complete the velocity-time graph below for the motion of the rocket until it reaches the ground.

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Answer

After the parachute opens, the rocket achieves a terminal velocity of 2.0 m/s almost instantly. This means the rocket will then have a horizontal line on the velocity-time graph from time = 4 seconds down to the time when it reaches the ground; the velocity remains constant at 2.0 m/s, reflecting the parachute's effect until the ground is reached.

Step 3

Determine the velocity of the rocket by drawing a scaled vector diagram.

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Answer

To find the resultant velocity of the rocket, we need to combine the vertical and horizontal components of the velocity.

The vertical velocity is 2.0 m/s downward and the horizontal velocity is 1.5 m/s. We can use the Pythagorean theorem to find the magnitude of the resultant velocity:

$V = \sqrt{(V_{vertical})^2 + (V_{horizontal})^2}$

Substituting the values gives:

$V = \sqrt{(2.0 m/s)^2 + (1.5 m/s)^2} = \sqrt{4 + 2.25} = \sqrt{6.25} = 2.5 m/s$

To determine the direction, we can use trigonometry:

$\theta = \tan^{-1}\left(\frac{V_{vertical}}{V_{horizontal}}\right) = \tan^{-1}\left(\frac{2.0}{1.5}\right) \approx 53^{\circ}$

Thus, the velocity of the rocket can be represented as a vector at an angle of approximately 53° to the horizontal.

A model rocket accelerates vertically upwards then decelerates due to gravity until it reaches a maximum height - Edexcel - A-Level Physics - Question 10 - 2023 - Paper 1

Worked Solution & Example Answer:A model rocket accelerates vertically upwards then decelerates due to gravity until it reaches a maximum height - Edexcel - A-Level Physics - Question 10 - 2023 - Paper 1

Show that the rocket reaches a maximum height of about 68 m.

Complete the velocity-time graph below for the motion of the rocket until it reaches the ground.

Determine the velocity of the rocket by drawing a scaled vector diagram.

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