What is the magnitude of its horizontal component

Question

Assignment:

Question 1. A vector representing 190 N is oriented at 34^? with the horizontal.

What is the magnitude of its horizontal component?

Question 2. What is the magnitude of its vertical component?

Question 3. A truck travels 1890 m uphill along a road that makes a constant angle of 4.68^? with the horizontal.

Find the magnitude of the truck's horizontal component of displacement.

Question 4. Find the magnitude of the truck's vertical component of displacement.
 
Question 5. A particle starts from the origin at t = 0 with an initial velocity having an x component of 25.8 m/s and a y component of -16.1 m/s.

The particle moves in the xy plane with an x component of acceleration only, given by 3.38 m/s².

Determine the x component of velocity after 7.75 s.

Question 6. Find the speed of the particle after 7.75 s.

Question 7. Find the magnitude of the displacement vector of the particle after t = 7.75 s.
 
Question 8. Vector A? is 2.98 units long and points in the positive y direction. Vector B? has a negative x component 4.5 units long, a positive y component 4.22 units long, and no z component.

Find A? · B? .

Question 9. What is the angle between A? and B? ?

Question 10. Given: Two vectors

A? = A_xˆi + A_yˆ?

and

B? = B_xˆi + B_yˆ?,

where A_x = -2, A_y = 3, B_x = 2, and B_y = 3.

Find the z component of A? × B? .

Question 11. Find the angle between A? and B. ?

Question 12. Given: Two vectors

A? = Ax ˆi + Ay ˆ

and

B? = B_xˆi + B_yˆ?,

where A_x = -2, A_y = 8.4, B_x = 2, and

By = 8.

Find the z component of A? × B? .

1. 0.8

2. 63.2

3. -32.8

4. -71.2

Question 13. The weight of a ball rolling down an inclined plane can be broken into two vector components: one acting parallel to the plane, and the other acting perpendicular to the plane.

At what angle of inclination of the plane are these two components equal?
 
Question 14. At what angle of inclination of the plane will the parallel component be equal to zero?
 
Question 15. At what angle of inclination of the plane will the parallel component be equal to the weight?

Question 16. Given: Two vectors

A? = A_xˆi + A_yˆ?

and

B? = B_xˆi + B_yˆ?,

where A_x = -2, A_y = 3, B_x = 2, and B_y = 3

Find the z component of A? × B? .

Question 17. A ship is expecting to travel to its home port 420 km due East. Before the ship starts to travel, a severe storm comes up and blows the ship 450 km due South.

How far is the ship from its home port?

Question 18. Consider: East to be 0? and North 90?.

At what angle North of East must the ship travel to reach its destination?

Question 19. A camel sets out to cross the desert, which is 44.1 km wide in the north-south direction.

The camel walks at the uniform speed 4.24 km/hr along a straight line in the direction 59^? north of East (only the camel knows why he chose that particular direction).

How long will it take the camel to cross the desert?

Question 20. Calculate the camel's eastward displacement while he crosses the desert.