1. 8-2B: Vectors Name:_________________ Hour: ________
Pre-Calculus
8-2B: Vectors
Name:_________________
Hour: ________
#’s I had trouble with: _________________
The vectors a and b represent two forces acting at the same point, and 𝜽 is the smallest positive angle between a and b. Approximate the magnitude of the resultant force.
1) 𝒂 =40 𝑙𝑏, 𝒃 =70 𝑙𝑏, 𝜃=45° ) 𝒂 =2.0 𝑙𝑏, 𝒃 =8.0 𝑙𝑏, 𝜃=120°
The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector.
3) (a) 90 𝑙𝑏, 𝑁75°𝑊 (b) 60 𝑙𝑏, 𝑆5°𝐸 ) (a) 6.0 𝑙𝑏, 110° (b) 2.0 𝑙𝑏, 215°
Approximate the horizontal and vertical components of the vector that is described.
A quarterback releases a football with ) The biceps muscle, in supporting the
a speed of 50 ft/sec at an angle of 35° forearm and a weight held in the hand,
with the horizontal exerts a force of 20 pounds. The muscle makes an angle of 108° with
the forearm.

2. Find a unit vector that has (a) the same direction as the vector a and (b) the opposite direction of the vector a.
7) a = -8i + 15j ) a = 2, −5
9) Find a vector that has the same direction as −8,2 and twice the magnitude.
10) Find a vector of magnitude 6 that has opposite direction of a = 4i – 7j.
11) Two tugboats are towing a large ship into port, as shown in the figure. The larger tug exerts a force of 4000 pounds on its cable, and the smaller tug exerts a force of 3200 pounds on its cable. If the ship is to travel on a straight line l, approximate the angle 𝜃 that the larger tug must make with l.
12) An airplane with an airspeed of 200 mph is flying in a direction of 50°, and a 40 mph wind is blowing directly from the west. True course is the direction of the (plane vector + wind vector) and the ground speed is the magnitude of that vector. Approximate the true course and ground speed.
13) An airplane pilot wishes to maintain a true course in the direction 250° with a ground speed of 400 mph when the wind is blowing directly north at 50 mph. Approximate the required airspeed and compass heading.