Scalars And Vectors
Which of the following correctly lists only scalar quantities?
A delivery drone flies 60 m due south and then 80 m due west. What is the magnitude of the drone’s resultant displacement?
A force vector is given by F⃗ = 5î − 12ĵ N. What is the magnitude of this force?
An object moves at 6 m/s along the negative x-axis. A student writes the velocity as v = −6 m/s. Which statement correctly interprets the negative sign?
Two vectors are defined as A⃗ = −4î + 3ĵ m and B⃗ = 6î + 1ĵ m. What is the resultant vector R⃗ = A⃗ + B⃗?
A jogger runs 3 km north, then 3 km south, returning to the starting point. The total time is 30 minutes. Which pair of values correctly describes the jogger’s average speed and average velocity?
The position vector of a particle is r⃗ = 3î + 4ĵ m. What is the unit position vector r̂?
A resultant vector has components Rₓ = −5 m and Rᵧ = −5 m. What is the direction of this vector measured counterclockwise from the positive x-axis?
A rescue helicopter hovers directly above a stranded hiker in a canyon. The pilot reports the hiker’s position as “200 m below.” A physics student argues this statement is incomplete as a vector description. Which additional piece of information would make this a complete vector quantity?
An object has a velocity of v⃗ = 7î − 24ĵ m/s. What is the speed of the object?
A student writes the following vector: F⃗ = 10 N at 53° north of east. Which unit vector expression is equivalent to this vector? (Use sin 53° ≈ 0.8, cos 53° ≈ 0.6)
A car drives 12 km east, then 5 km north. A second car drives 13 km northeast in a straight line. Which statement correctly compares the two trips?
A projectile is launched and, at a particular instant, has velocity components vₓ = −3 m/s and vᵧ = 4 m/s. An observer claims the projectile is “moving at 1 m/s.” Is this claim consistent with how vector magnitudes are determined?
The unit position vector r̂ appears in equations for gravitational and electric fields. What distinguishes r̂ from the position vector r⃗?
An elevator accelerates downward at 2 m/s² while a passenger inside is moving downward at 5 m/s. Taking upward as the positive direction, which set of signs correctly represents the passenger’s velocity and acceleration?
A physics student must add three force vectors: F⃗₁ = 2î − 3ĵ N, F⃗₂ = −5î + 1ĵ N, and F⃗₃ = 4î + 2ĵ N. What is the magnitude of the resultant force?
A swimmer crosses a river by swimming 80 m due north while the current carries her 60 m due east. She claims her displacement is “140 m northeast.” Identify the error in her claim and determine the correct displacement magnitude and direction.