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# A Rocket Modelled by a Particle: S-Axis, Maximum Height, Etc.

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A rocket is modelled by a particle that moves along a vertical line. From launch, the rocket rises until its motor cuts out after 13 seconds. At this time it has reached a height of 490 metres above the launch pad and attained an upward velocity of 70ms−1. From this time on, the rocket has a constant upward acceleration of −10 m s−2 (due to the effect of gravity alone).

(a) Choose the s-axis (for the position of the particle that represents the rocket) to point upwards, with origin at the launch pad. Take t = 0 to be the time when the rocket motor cuts out.
(i) What is the maximum height (above the launch pad) reached by the rocket?
(ii) How long (from launch) does the rocket take to reach this maximum height?

(b) After how long (from launch) does the rocket crash on to the launch pad? Give your answer in seconds, correct to one decimal place.

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#### Solution Preview

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First we make a quick sketch of the rockets motion as shown below

(a)
(i) From the point of origin ( the point where the rocket motor stops firing) the rocket then is only subject to de-acceleration due to gravity so we can apply the equation  below from linear kinematics to determine the vertical distance the rocket travels before it stops its ascent. This is the maximum distance above point

We write



Where is the velocity of the rocket at the top of its ascent (ie, ...

#### Solution Summary

A rocket modeled by a particle for S-Axis and the maximum heights.

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