MIDTERM PROBLEM SET



MIDTERM PROBLEM SET

PHYSICS 13E

1. A square field measuring 100.0 m by 100.0 m has an area of 1.00 hectare. An acre has an area of 43,600 ft2. If a country lot has an area of 12.0 acres, what is the area in hectares?

2. The following conversions occur frequently in physics and are very useful. (a) Use 1 mi = 5280 ft and 1 h = 3600 s to convert 60 mph to units of ft/s. (b) The acceleration of a freely falling object is 32 ft/s2.Use 1 ft = 30.48 cm to express this acceleration in units of m/s2. (c) The density of water is 1.0 g/cm3. Convert this density to units of kg/m3.

3. Find the magnitude and direction of the vector represented by the following pairs of components: (a) Ax = -8.60 cm, Ay = 5.20 cm; (b) Ax = -9.70 m, Ay = -2.45 m; (c) Ax = 7.75 km, Ay = -2.70 km.

4. Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 25.0° west of north, and the resultant of these two pulls is 460.0 N directly northward. Use vector components to find the magnitude of each of these pulls and the direction of the smaller pull.

5. At Enormous State University (ESU), the football team records its plays using vector displacements, with the origin taken to be the position of the ball before the play starts. In a certain pass play, the receiver starts at +1.0î – 5.0ĵ where the units are yards, î is to the right, and ĵ is downfield. Subsequent displacements of the receiver are + 9.0î (in motion before the snap), + 11.0ĵ (breaks downfield), – 6.0î + 4.0ĵ (zigs), and + 12.0î + 18.0ĵ (zags). Meanwhile, the quarterback has dropped straight back to a position – 7.0ĵ. How far and in which direction must the quarterback throw the ball? (Like the coach, you will be well advised to diagram the situation before solving it numerically.)

6. You are given vectors [pic] and[pic]. A third vector [pic] lies in the xy-plane. Vector [pic] is perpendicular to vector [pic] and the scalar product of [pic] with [pic] is 15.0. From this information, find the components of vector[pic].

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