(Note) For these examples, we will stick with speeds much less than the speed of light (3x10⁸ m/s). At those faster speeds, things get really weird and we have to use Einstein's formulae for Special Relativity.

1. Consider Bob. Bob is running on a train at 3 m/s [E] relative to the train. The train is moving at 5 m/s [E] relative to the ground. What is Bob's velocity relative to Ernie who is sitting stationary on the ground as the train passes by?

(Two Dimension) Please visit this simulation:ophysics.com/k11.html

1. Set the velocity of the river relative to the Earth to zero. Aim the boat directly across the river (aim direction is 0). Note how long it takes to cross the river (to 1 decimal place).

2. What happens to the crossing time if you now add a river velocity, but keep the boat velocity and aim direction the same?

3. Keeping the Boat and river velocity constant, change the aim direction to upstream (towards the West/left) and downstream (towards the East/right) and directly across. What happens to the time to cross depending on the heading?

4. If you set the river velocity to 3m/s, the boat velocity to 4 m/s, and you set the aim direction to zero, what happens to the boat as it crosses the river? What is the velocity of the boat relative to the earth in this case? What is the time to cross the river?

5. Keeping the river and boat velocities at 3 m/s and 4 m/s respectively, what heading must the boat have in order to cross directly across the river? What is the time to cross in this case compared to the time from step 5?

6.Based on this simulation, what direction should you head the boat to have the quickest crossing time? In order to have the quickest time, what is the sacrifice you will have to make in terms of ending location?