Vectors and Projectiles: Audio Guided Solution

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Mechanics: Vectors and Projectiles

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Vectors and Projectiles: Audio Guided Solution

Problem 10:

Consider the map of the United States below. Given the scale that 1 cm = 340 km, a protractor and a ruler can be used to determine the magnitude and direction for the following trips. All directions are expressed using the counter-clockwise from east convention. For each trip, use the sine, cosine and tangent functions to determine the horizontal and vertical components of the displacement. Be sure to indicate E, W, N, or S as the direction for each component.

Trip	Displacement	Horiz. Component	Vert. Component
Chicago to Denver	1430 km, 187°
Reno to Miami	4030 km, 341°
Seattle to Washington	3480 km, 344°
Houston to Salt Lake City	2040 km, 143°

Audio Guided Solution

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Set A: ∑F = 16 N, right
Set B: ∑F = 14 N, left
Set C: ∑F = 4 N, up

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Trip	Displacement	Horiz. Component	Vert. Component
Chicago to Denver	1430 km, 187°	1419 km, West	174 km, South
Reno to Miami	4030 km, 341°	3810 km, East	1312 km, South
Seattle to Washington	3480 km, 344°	3345 km, East	959 km, South
Houston to Salt Lake City	2040 km, 143°	1629 km, West	1228 km, North

Habits of an Effective Problem Solver

Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., v_ox = 12.4 m/s, v_oy = 0.0 m/s, d_x = 32.7 m, d_y = ???.
Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
Identify the appropriate formula(s) to use.
Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.

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