FSG Exercises Konstantinos 2

I walk down a long street at 1 m s−1 for an hour. During this time I count the number of trams that pass me by. Knowing that they follow a regular timetable in both directions I am initially surprised to note that only 15 trams overtake me, whereas 20 passed me head-on. What is the average speed of the trams? (Answer in m/s I.e. 12)

Hayley and Rob offer to paint the outside of our house. Hayley claims she can do the job in 2 days (working continuously). Rob says he’ll complete the job in 3 days. If they are both hired to work together, how long should it take? (i.e. 5.7)

A ball is at rest at the top of a frictionless hill. It is then given a slight nudge and speeds up to 4 ms−1 at the bottom of the hill. If the ball had a speed of 3 ms−1 at the top of the hill (instead of being stationary), what would its speed now be at the bottom? (Answer in m/s I.e. 12)

A 10×10×10 cube is constructed from a thousand unit cubes. How many of the unit cubes have at least one face on the surface of the larger cube? (i.e. 1522)

It’s finally time for a battle to end the long-running dispute between pirates and ninjas. They face off at 90 m. The pirate limps towards the ninja at 2 m s−1 , while the ninja glides towards the pirate at twice the speed. It is only a matter of time before they collide and crush the loyal parrot which repeatedly flies back and forth at a constant speed of 8 m s−1 , elastically bouncing off the two. What is the total distance the parrot travels before being crushed?