Consider Think and Solve Problem #1a on p. 42 of the text:
"A boat is rowed at 8 km/h directly across a river that flows at 6 km/h... What is the resultant speed of the boat?"
(The problem of combining velocities in two dimension is also discussed in section 3.2 Velocity Vectors, on p. 30 of the text. In particular, see Fig. 3.3)
The phrase "boat is rowed at 8 km/h" means that the speedometer of the boat measures the boat's speed relative to the water, so that if there is no current the boat's speed relative to the riverbank will be 8 km/h. Of course, the speed of the water (current) is measured relative to the riverbank.
The text says that the answer to the above question is 10 km/h at an angle of 37o from the original direction of the boat. The answer is arrived at as shown at right. This means that:
velocity of boat relative to the riverbank = velocity of boat relative to the water + velocity of water relative to the riverbank
where we need to remember that the "+" sign above refers to vector addition.
The question is, does all of this really work? In this lab, you can simulate this situation using a motorized cart to represent the boat and a large piece of paper to represent the water. The lab table can represent the riverbank.
variable-speed motorized cart |
meter stick or metric tape |
stop watch |
2 meters of bulletin-board paper |
Design an experiment that will test the text's claim concerning the way velocities add in two dimensions. Some suggested equipment is listed above - you don't have to use all of it, and if you will need additional equipment contact your instructor. Be sure to discuss your plans with your instructor before you begin.