Review the following concepts if necessary:

### Problems

- A canoe is paddled due north across a lake at 2.0 m/s relative to still water. The current in the lake flows toward the east; its speed is 0.5 m/s. Which of the following vectors best represents the velocity of the canoe relative to shore?
- Force vector
has magnitude 27.0 N and is direction 74° from the vertical, as shown above. Which of the following are the horizontal and vertical components of vector*A*?*A* - Which of the following is a scalar quantity?

### Solutions

1. **B** - To solve, add the northward 2.0 m/s velocity vector to the eastward 0.5 m/s vector. These vectors are at right angles to one another, so the magnitude of the resultant is given by the Pythagorean theorem. You don't have a calculator on the multiple choice section, though, so you'll have to be clever. There's only one answer that makes sense! The hypothenuse of a right triangle has to be bigger than either leg, but less than the algebraic sum of the legs. Only B, 2.1 m/s, meets this criterion.

2. **A** - Again, with no calcultor, you cannot just plug into the calculator (though if you could, careful: the horizontal component of **A** is 27.0 N cos 16º is the angle from the horizontal.) Answer B and E are wrong because the vertical component is bigger than the horizontal component, which doesn't make any sense based on the diagram. Choice C is wrong because the horizontal component is bigger than the magnitude of vector itself - ridiculous! Same problem with choice D, where the horizontal component is equal to the magnitude of the vector. Answer must be A.

3. **D** - A scalar has no direction. All forces have direction, including weight (which is the force of gravity). Mass is just a measure of how much stuff is contained in an object, and thus has no direction.

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