(a) What is the direction of this vector? Give your answer as an angle measured

Question

(a) What is the direction of this vector? Give your answer as an angle measured counterclockwise from the +x direction.
°

(b) What is the magnitude of this vector?
m

(c) If you doubled both the x and y components of this vector, how would the answers to parts (a) and (b) change?

a. The direction of the vector would rotate clockwise by an angle equal to twice the angle measured counterclockwise from +x, but the magnitude would remain the same.

b. The direction would remain the same, but the magnitude would increase by a factor of 4.

c. The angle counterclockwise from +x would increase by a factor of 2, but the magnitude would remain the same.

d. The direction would remain the same, but the magnitude would increase by a factor of 2.

  2. A cross-country runner has a speed of 4.00 m/s and runs in a direction 15.0° counterclockwise from the positive x-axis.(a) What are the components of the runner's velocity?

(b) If the runner slows down until his speed is half of the original speed, how will it affect the components of his velocity?

a.His velocity components will be quadrupled.

b. His velocity components will be quartered.     

c. His velocity components will be halved.

d. His velocity components will not change.

3. A baseball pitcher throws a ball horizontally at a speed of 43.6 m/s. A catcher is 19.0 m away from the pitcher. Find the magnitude of the vertical distance that the ball drops as it moves from the pitcher to the catcher. Ignore air resistance.

m

4. A kid on the top of a building 32 m tall throws a ball at 19 m/s at an angle of 50 degrees above the horizontal. How far from the base of the building does the ball land? (Assume the ground is level.)

m

5.You drive 8.00 km in a straight line in a direction 10° East of North.(a) Find the distances you would have to drive straight East and then straight North to arrive at the same point. (This is equivalent to finding the components of the displacement along the East and North directions.)

km East
km North
(b) Show that you still arrive at the same point if the East and North legs are reversed in order.

6. Suppose you walk 18.0 m straight west and then 25.0 m straight north.

How far are you from your starting point?
m
What is the compass direction of a line connecting your starting point to your final position?
° west of north

(If you represent the two legs of the walk as vector displacements A and B, as in Figure 3.23, then this problem asks you to find their sum R = A + B).

7. An owl carrying a mouse is flying at 19 m/s horiztonally, at 34 m above the (level) ground. If the owl drops the mouse, how far horizontally will the mouse travel before it hits the ground?

m

8. You are walking around your neighborhood and you see a child on top of a roof of a building kick a soccer ball. The soccer ball is kicked at 37° from the edge of the building with an initial velocity of 13 m/s and lands 61 meters away from the wall. How tall is the building that the child is standing on?

m

9. A new landowner has a triangular piece of flat land she wishes to fence. Starting at the west corner, she measures the first side to be 80 m long and the next to be 105 m -- these sides are represented as displacement vectors A and B in Figure 3.26, where 1=23°, and 2=12°. She then correctly calculates the length and orientation of the third side C. What is her result?

m  ° south of west

10. While standing on the roof of a building, a child tosses a tennis ball with an initial speed of 16 m/s at an angle of 30° below the horizontal. The ball lands on the ground 2.9 s later. How tall is the building?

m

11.A vector

has a magnitude of 3 units and points in the y direction, while a vector

has one quarter the magnitude of

and points in the +x direction. What are the magnitude and direction of the following vectors? Give the directions of each as an angle measured counterclockwise from the +x direction.(a)    

(b)    

(c)    

12. A football is kicked from ground level with an initial velocity of 21.0 m/s at angle of 43.0° above the horizontal. How long is the football in the air before it hits the ground? Ignore air resistance.

s

Explanation / Answer

a)

rx = 13.9

ry = 8.9

the direction of the vectors is

tan(theta) = ry / rx

theta = tan^-1(8.9 / 13.9)

theta = 32.63 deg

counterclockwise to the positive x direction is = 32.63 + 180 = 212.63 deg

b)

the magnitude of the vector is

R = sqrt(rx^2 + ry^2)

R = sqrt( 13.9^2 + 8.9^2)

R = 16.5 m

c)

if we doubles the vectors

rx = 27.8

ry = 17.8

then the direction is

theta = tan^-1( 17.8 / 27.8 )

theta = 32.63 deg

then counterclockwise to the positive x direction is 212.63 deg

then the magnitude is

R = sqrt( 27.8^2 + 17.8^2)

R = 33.01 m

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.