Question

For his engineering project, Fran¸cois built a model rocket of mass m = 0.55 kg simply by using materials he found lying around the lab and blueprints he found on the internet. The rocket’s propulsion is provided by a special battery-powered fan that is able to provide a constant force |Ffan| = 7.0 N – that is, once it is launched in a specific direction, the direction of the fan’s force does not change. The downside is that the rocket will use up its entire power supply in 6.0 s. The rocket is coated with a noncaloric silicon-based kitchen lubricant, so we can assume that air resistance does not affect its motion.

(a) Suppose the rocket is launched vertically upwards from rest. Draw the free-body diagram (1 mark) and calculate the magnitude of the net force acting on the rocket (1 mark) before the power runs out.

(b) How high does the rocket fly before losing power? (1 mark) What is its velocity at this point? (1 mark)

(c) Calculate the maximum height of the rocket.

(d) Next, suppose instead that the rocket is launched from rest at an angle θ from the horizontal axis. Write down the equations describing the rocket’s horizontal (x(t)) and vertical (y(t)) motion as a function of time (1 mark) and draw an appropriate free-body diagram (1 mark).
(e) Calculate the minimum angle for which the rocket will takeoff from rest. (2 marks

Answer 1