Question

Fig 3.1 shows the speed-time graph of a firework rocket as it rises and then falls to the ground
2
rocket
moving
upwards
speed
B
time
rocket
moving
downwards
Fig. 3.1
The rocket runs out of fuel at A It reaches its maximum height at B. Al Elt returns to the ground,
(a) (0) Starte the gradient of the graph at B. gradient
......11
00 State why the gradient has this value at B.
111

Answer 1

The acceleration of an object in free fall motion is the constant acceleration due to gravity

(i) The gradient of the rocket at point B is approximately -9.81 m/s²

(ii) The reason why the gradient is -9.81 m/s² is as follows;

The given graph is the speed to time graph with the upward direction taken as positive

• Gradient of the speed to time graph is the acceleration

Given that at point B the object is at the maximum point, the upward motion due to the rocket stops, the motion of the rocket is then due to gravity

Therefore, the gradient at B, is given as follows;

$Gradient = \dfrac{\Delta v}{\Delta t } = \dfrac{d(u + a \cdot t)}{dt} =a$

• Force = Mass × Acceleration

At point B the only force acting on the rocket is the force of gravity, therefore, the acceleration of the rocket at B, a = g, acceleration due to gravity ≈  9.81 m/s², and the rocket is falling due to its weight

• Force acting at B = Weight = Mass × Acceleration due to gravity, g

Therefore, only gravitational force is acting on the rocket when the direction of the rocket changes and rocket falls freely, at B, and the acceleration of the rocket at B = g = 9.81 m/s²

Learn more about free fall motion here:

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