vectors

/in /by

Two vectors have length V1 = 3.5 km and V2 = 4.2 km .

  • What is the maximum magnitude of their vector sum?

Express your answer using two significant figures.

  • What is the minimum magnitude of their vector sum?

Express your answer using two significant figures.

QUESTION 3

A car is driven 225 km west and then 78 km southwest 45∘.

Part a

What is the magnitude of displacement of the car from the point of origin?

Express your answer using two significant figures.

Part b

What is the direction of displacement of the car from the point of origin?

Express your answer using two significant figures.

Part c

Draw a diagram.

Draw  the vectors with theirs tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will be graded.

QUESTION 4

If Vx = 7.70 units and Vy = -6.00 units, determine (a)the magnitude and (b)direction of V⃗ .

QUESTION 5

An airplane is traveling 835 km/h in a direction 41.5 ∘ west of north. (Figure 1)

Part a

Find the component of the velocity vector in the northerly direction.

Part b

Find the component of the velocity vector in the westerly direction.

Part c

How far north has the plane traveled after 2.70 h ?

Part d

How far west has the plane traveled after 2.70 h ?

QUESTION 6

Figure

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Part a

For the vectors shown in (Figure 1), determine B⃗ −2A⃗ .Caption: Vector magnitudes are given in arbitrary units.

Express your answer in terms of the unit vectors i^ and j^. To denote vectors in your answers, be sure to select the ‘unit vector’ button.

Part b

For the vectors shown in the figure, determine 2A⃗ −3B⃗ +2C⃗ . Caption: Vector magnitudes are given in arbitrary units.

Express your answer in terms of the unit vectors i^ and j^. To denote vectors in your answers, be sure to select the ‘unit vector’ button.

QUESTION 7

Figure

1 of 1

Part a

For the vectors given in the figure, determine A⃗ −B⃗ +C⃗ . (Figure 1)

Express your answer using three significant figures separated by a comma.

Part b

For the vectors given in the figure, determine A⃗ +B⃗ −C⃗ .

Express your answer using three significant figures separated by a comma.

Part c

For the vectors given in the figure, determine C⃗ −A⃗ −B⃗ .

Express your answer using three significant figures separated by a comma.

QUESTION 8

The position of a particular particle as a function of time is given by

r⃗  = ( 9.60ti^ + 8.85j^ – 1.00t2k^)m, where t is in seconds.

Part a

Determine the particle’s velocity as a function of time.

Express your answer in terms of the unit vectors i^, j^, and k^.

Part b

Determine the particle’s acceleration as a function of time.

Express your answer in terms of the unit vectors i^, j^, and k^.

QUESTION 9

A skier is accelerating down a 30.0 ∘∘ hill at 1.80m/s2m/s2.

Figure

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Part a

What is the vertical component of her acceleration?

Part b

How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 300 m ? (Figure 1)

QUESTION 10

An ant walks on a piece of graph paper straight along the x axis a distance of 10.0 cm in 2.10 s . It then turns left 30.0 ∘ and walks in a straight line another 10.0 cm in 1.80 s . Finally, it turns another 70.0 ∘ to the left and walks another 10.0 cm in 1.50 s .

Part a

Determine the x component of the ant’s average velocity.

Part b

Determine the y component of the ant’s average velocity.

Part c

Determine the magnitude of ant’s average velocity.

Part d

Determine the direction of ant’s average velocity.

QUESTION 11

Suppose the position of an object is given by r⃗  = (3.0t2i^ – 6.0t3j^)m. Where t in seconds.

Part a

Determine its velocity v⃗  as a function of time t.

Express your answer using two significant figures. Express your answer in terms of the unit vectors i^ and j^.

Part b

Determine its acceleration a⃗  as a function of time t.

Express your answer using two significant figures. Express your answer in terms of the unit vectors i^ and j^.

Part c

Determine r⃗  at time t = 2.5 s.

Express your answer using two significant figures. Express your answer in terms of the unit vectors i^ and j^.

Part d

Determine v⃗  at time t = 2.5 s.

Express your answer using two significant figures. Express your answer in terms of the unit vectors i^ and j^.