Section 2 review
When studying motion in two dimensions, we need to specify two numbers to describe a displacement, velocity, or acceleration vector. The two numbers can be x and y (Cartesian) coordinates or a magnitude and an angle (polar coordinates). The resultant (sum) of two or more vectors can be calculated by separately adding the vectors’ Cartesian coordinates. When a boat is rowed across a flowing river, or an airplane flies in windy air, the vehicle’s velocity must be added to the current or wind vector to predict how the motion will appear from the ground. Read the text aloud
displacement, polar coordinates, Cartesian coordinates, compass, velocity, speed, acceleration

a = Δ v Δt

Review problems and questions

What vector sum will displace the car from its starting point to the target?
  1. A programmable toy car has to reach the target shown here. Which of the following vector sums will displace the car from its starting point to the target?
    1. (1, 5) m + (2, −3) m + (3, 1) m
    2. (3, 1) m + (2, −2) m + (1, 3) m
    3. (1, 4) m + (2, −2) m + (3, 3) m Read the text aloud Show
Match each vector with its polar coordinate equivalent
  1. Match each of the labeled vectors (a through d) with one of the following expressions, given in polar coordinates. (Each square on the grid represents one meter of displacement.)
       (i) (2 m, 90°)    (ii) (5 m, −30°)    (iii) (7 m, 45°)    (iv) (3 m, 120°) Read the text aloud Show
  1. A rowboat rests on the southern bank of a river 20 m wide flowing west to east. The rowboat is moored 60 m west of a treacherous waterfall. Jamie rows the boat at a speed of 2 m/s northward with respect to the flowing water. The current flows at a rate of 4 m/s eastward, which is the water’s velocity with respect to the ground. Jamie enters the boat and begins to row.
    1. Sketch a diagram of the scenario (as seen from above), with the velocity vectors oriented correctly and drawn to scale.
    2. What is the boat’s velocity (in meters per second) with respect to the ground? (Provide components as well as the speed and approximate compass heading.)
    3. Can Jamie reach the northern riverbank before the current carries him into the waterfall? Read the text aloud Show

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