physics vectors
A baby toddles 3 m west and 2 m south. If θ = tan-1(⅔), the baby's resultant displacement will be oriented counterclockwise at angle θ from which axis? Assume east and north lie along the +x-axis and +y-axis, respectively.
- x-axis
If the magnitude of a vector component equals the magnitude of the vector, then what is the magnitude of the other vector component?
0
How can you use the Pythagorean theorem to add two vectors that are not perpendicular?
1.Resolve each vector into perpendicular components; 2.Add the components that lie along the same axis 3.The resultant component vectors can be added by using the pythagorean theorem because they are perpendicular
What is a vector quantity?
A physical quantity the can be added in any order, has a magnitude, and a direction
What is a scalar quantity?
A physical quantity with magnitude no direction
What is a resultant?
A sum of two or more vectors
Which is a scalar quantity, instantaneous velocity or average speed?
Average speed
What is a projection of a vector along an axis of a coordinate system called?
Components of a vector
Which is a vector quantity, distance or displacement?
Displacement, has both magnitude and direction
Breaking a vector into two components is given what term?
Resolution of vector
If the magnitude of a vector component equals zero, what is the magnitude of the other vector component?
The magnitude of the vector
In a coordinate system, a vector is oriented at angle θ with respect to the x-axis. The x component of the vector equals the vector's magnitude multiplied by which trigonometric function? a.cos θ c.sin θ b.cot θ d.tan θ
a.cos θ
A car travels down a road at a certain velocity, vcar. The driver slows down so that the car is traveling only half as fast as before. Which of the following is the correct expression for the resulting velocity? a. 2Vcar c. - ½Vcar b. ½Vcar d. -2Vcar
b. 1/2Vcar
A football player runs in one direction to catch a pass, then turns and runs twice as fast in the opposite direction toward the goal line. Which of the following is a correct expression for the original velocity and the resulting velocity? a. -Vplayer -2Vplayer c. Vplayer -2Vplayer b. Vplayer 2Vplayer d. 2Vplayer -Vplayer
c. Vplayer -2Vplayer
In a coordinate system, a vector is oriented at angle θ with respect to the x-axis. The y component of the vector equals the vector's magnitude multiplied by which trigonometric function? a. cos θ c. sin θ b. cot θ d. tan θ
c. sin θ
Which of the following is the best coordinate system to analyze a painter climbing a ladder at an angle of 60° to the ground? a.x-axis: horizontal along the ground; y-axis: along the ladder b.x-axis: along the ladder; y-axis: horizontal along the ground c.x-axis: horizontal along the ground; y-axis: up and down d.x-axis: along the ladder; y-axis: up and down
c.x-axis: horizontal along the ground; y-axis: up and down
A student walks from the door of the house to the end of the driveway and realizes that he missed the bus. The student runs back to the house, traveling three times as fast. Which of the following is the correct expression for the return velocity if the initial velocity is Vstudent? a. 3Vstudent c. -⅓ Vstudent b. ⅓ Vstudent d. -3Vstudent
d. -3Vstudent
The length of a vector arrow in a diagram is proportional to what property of the vector?
magnitude
If the magnitude of a vector component is the magnitude of the vector, what is the orientation of the vector with respect to that axis?
parallel
If the magnitude of a vector component is zero, what is the orientation of the vector with respect to that axis?
perpendicular
The equation d = √(x2 + y2 ) is valid only if Δx and Δy are magnitudes of vectors that have what orientation with respect to each other?
perpendicular
The displacement, −2.0 m north, represents a positive displacement in which direction?
south
Is the quantity viΔt a scalar quantity or vector quantity?
vector
Is the quantity 𝚫vi / Δt a scalar quantity or vector quantity?
vector
The component Ax of a vector A lies along what axis?
x-axis