2 . Force vector A 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?
3 . Which of the following is a scalar quantity?
(A) electric force
(B) gravitational force
(C) weight
(D) mass
(E) frictionSolutions to Practice Problems
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 hypotenuse 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 calculator, you cannot just plug numbers in (though if you could, careful: the
horizontal component of A is 27.0 N cos 16° because 16° is the angle from the horizontal). Answers 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 the vector itself—ridiculous! Same problem with choice D, where the
horizontal component is equal to the magnitude of the vector. So the 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.