L6FM M1 Homework 1

To be handed in on paper.

1. A rocket is propelled vertically up from the ground with speed $8.1 ms^{-1}$. Find

1. The maximum height reached by the rocket
2. The total time the rocket is in the air
3. State one assumption you made

[6 marks]

2. A car is travelling between 2 sets of traffic lights 510m apart. It accelerates from the first set of lights with constant acceleration $3ms^{-2}$ from rest until it reaches a constant speed of $15.6ms^{-1}$. It travels at this speed for T seconds and then decelerates uniformly at $6ms^{-2}$, coming to a stop at the second set of traffic lights.

1. Draw a (t,v) graph
2. Calculate the value of T

[6 marks]

3. A lemming projects himself down from the top of a 200m cliff at $2ms^{-1}$. At the same instant another lemming is fired up from directly below with a speed of $73ms^{-1}$. The two lemmings collide. Calculate after how long this happens and how far from the bottom of the cliff this is. (Sorry this question has been changed due to a typo in the speed of the second lemming)

[6 marks]

4. Travelling along the motorway at 67mph, I notice a car approaching in the rearview mirror. It is approximately quarter of a mile behing me. After 6 minutes it passes me. What speed it the car travelling at?

[2 marks]

5. A firework lets out a green spark from the ground which travels upwards at $10.6ms^{-1}$. After 0.2 seconds it emits a red spark which travel upwards at $15ms^{-1}$. After how long from the green spark being released do the red and green sparks collide?

[4 marks]