Physics 40S
Extra Exercises – Vectors – Use components of vectors, where needed.
1. You decide to swim across a river flowing at 2.2 m/s South. If you swim at
1.5 m/s due West, what is your resultant velocity?
2. An airplane sets its course at a bearing of [S50°W] and a cruising speed
of 250 km/hr. The wind is blowing towards [W16N°] at a speed of 30
km/hr. What is the resultant velocity of the airplane?
3. Canadian golf pro Mike Weir launches a golf ball at the green at 20 m/s.
The green is due North from him. A cross wind to the East is blowing at 7
m/s. What is the resultant velocity of the golf ball?
4. An anthropologist finds a pirate's instructions to find some buried treasure.
The instructions say to start at a large rock, take 50 paces north, then 35
paces NW. How far away and in what direction from the rock is the buried
treasure?
5. A deep-sea diver is able to walk on the ocean floor at a speed of 0.2 m/s.
He walks at a bearing of [E30S] for 90 seconds, and then turns to a
bearing of [S25°W] and walks for 50 seconds. How far from his start point
and in what direction is the diver?
6. Myra is competing in an orienteering competition, gets lost, and loses her
compass. The directions were to walk 1.6 km [S 5 W], then 0.9 km [S 20°
W]. If she radios back to the start for help and determines that she
mistakenly walked the 0.9 km at [N 20 E], how far and in what direction
must a rescuer walk to find her?
7. A small airplane headed at [S45°W] is cruising at 150 km/hr. It encounters
a wind blowing towards [N15W] at 35 km/hr. What is the plane's resultant
velocity now?
Subtractions
1. Lisa is flying an ultra light aircraft with a maximum speed of 15 km/hr. She
sets her course at bearing [N15°W]. She flies for 1 hour at the maximum
speed and ends up 8 km, bearing [N8°W] from her start point. What was
her resultant velocity? What is the wind's velocity?
2. A robot-controlled submarine is sent under water to search an area for a
sunken ship. The submarine is programmed to travel at 2 m/s at a bearing
of [W25N]. If the submarine is located 800 m away from the stationary
mother ship after 7 minutes at a bearing of [N58W]°, what is the velocity
of the underwater current?
3. An airplane, whose air speed is 480 km/h, is supposed to fly in a straight
path [E 28° N]. However, a steady 100-km/h wind is blowing from the
north. In what direction should the plane head? (Draw a picture, no
components necessary – THINK!)
4. A ferryboat, whose speed in still water is 1.80 m/s must
cross a 260-m-wide river and arrive at a point 110 m
upstream from where it starts. To do so, the pilot must
head the boat at a 45° upstream angle.
a) Find the x and y components of the boat's
speed.
b) Find the time to cross the river.
c) Find the resultant velocity upstream.
d) What is the speed of the river's current?
5. A river is flowing due South at 2.8 m/s. Hannah wants to
row straight across (East) at a speed of 1.6 m/s. At what bearing and at
what speed must she row to go straight across?
Answers
1.
2.
3.
4.
5.
2.66 m/s @ [S 34.3 W]
267.9 km/hr @ [W35S]
21.2 m/s [N 19.3 E]
78.7 paces [W 71.7 N]
21.3 m [E 58 S]]
Subtractions
1.
2.
3.
4.
R = 8 km/hr [N 8 W]
7.17 km/hr [S 23 E]
0.28 m/s [E 45 N]
[N51 E]
a) bx = 2.02 m/s by = 2.02 m/s
b) 129 s
d) 1.17 m/s (left)
5. 3.22 m/s [E 60 N]
c) 0.85 m/s