# Chapter 6, 7.1 and 7.2

First Half of Chapter 6:  General Vectors Questions

Diagram for Question 1 is on right

1.          Given that the vector AD is equal to 3/5 of the vector BC, prove that the vector AE is equal to 5/8 of the vector AD plus 3/8 of the vector AB

Video Solution Chapter 7.1:  Force Questions

1.     Example 2 on Page 355 - Two forces of 20 N and 40 N act at an angle of 30 degrees to each other.  Determine the resultant of these two forces.

2.     Example 3 on Page 358 - Kayla pulls on a rope attached to her sleigh with a force of 200 N.  If the rope makes an angle of 20 degrees with the horizontal, determine:
a)          the force that pulls the sleigh forward
b)          the force that tends to lift the sleigh

Video Solution to Number 1 and 2 above

3.      A 75 kg mass is suspended from a ceiling by two lengths of rope that make angles of 50 degrees and 35 degrees with the ceiling.  Determine the tension in each rope.           Answer:  approx. 605 N up the rope that is 50 degrees to the ceiling, and approx. 475 N up the other rope.              Video Solution to Number 3

4.        Three forces of 7 Newtons, 9 Newtons and 12 Newtons are in equilibrium.  What is the angle between the two largest forces?      Answer:  144.6 degrees                Video Solution to Number 4 by Student.

Chapter 7.2:  Velocity Questions

1.     An airplane is traveling at a velocity of 450 km/h [S 20 degrees E] when it encounters a wind with a velocity of 140 km/h [N 40 degrees E].  What is the ground velocity of the airplane?            Answer:   approximately 398.9 km/h [S 37.7 degrees E]            video solution

2.     An airplane is traveling at a ground velocity of 320 km/h [N 15 degrees W] in a wind-free environment.  The plane then encounters a wind which changes its ground velocity to 340 km/h [N 35 degrees W].  What is the velocity of the wind?           Answer:   approximately 116.3 km/h [W 15.2 degrees S]          video solution

3.     An airplane is traveling S35oW with a ground speed of 270 km/h.  The nose of the plane is actually pointing S22oW with an airspeed of 262 km/h.  What is the velocity of the wind?         Answer:  Approximately 60.75 km/h, [E 69 degrees S]   video solution to Number 3 by student