Worksheet #4 – Vector Applications
1. An airplane is flying on a bearing of 170 at 460 mph. Find the component form of the
velocity of the airplane.
460cos280 ,460sin280  79.87, 453.01
2. A motorboat capable of 20 mph keeps the bow of the boat pointed straight across a milewide river. The current is flowing left to right at 8 mph. Find where the boat meets the
opposite shore.
0.4 miles downstream
3. An airplane is flying on a compass heading (bearing) of 170 at 460 mph. A wind is blowing
with the bearing 200 at 80 mph.
a. Find the component form of the velocity of the airplane.
460cos280 ,460sin280  79.87, 453.01
b. Find the actual ground speed and direction of the airplane.
Component Form of A & W : 460cos280  80cos250 ,460sin280  80sin250  52.52, 528.19
Groundspeed : v 
52.52   528.19
2
2
 530.79 mph
Direction Angle : 275.68
4. A basketball is shot at a 70 angle with the horizontal direction with an initial speed of 10
m/sec.
a. Find the component form of the initial velocity.
10cos70 ,10sin70  3.42,9.40
b. Give an interpretation of the horizontal and vertical components of the velocity.


Horizontal component is the (constant) horizontal speed of the basketball as it
travels toward the basket
Vertical component is the vertical velocity of the basketball, affected by both initial
speed and downward pull of gravity
Worksheet #4 – Vector Applications
5. Mr. League and his dog-walking spider monkey, Dingles, own a strong-willed puppy named
Winston. It is so hard to take Winston for a walk that they devise a scheme to use two
leashes. If Mr. League and Dingles pull with forces of 23 lb and 27 lb at the angles shown in the
figure, how hard is Winston pulling if the puppy holds Mr. League and Dingles at a standstill.
Mr. League
23 lb
18˚
Winston
15˚
27 lb
Dingles
23cos18  27cos15  47.95 lbs