Phys 221 SI Worksheet 1
Vectors
1. Add the following vectors and determine the resultant.
a. 6.0 m/s, 225 deg and 2.0 m/s, 90 deg Ans: -4.24i - 2.24j
b. 8 m/s, 90 deg and 5 m/s, 75 deg Ans: 1.29i + 12.83j
2. If |A| = 5 and |B| =3 and the angle between the two vectors is 30 degrees.
a. Calculate the magnitude of the dot product of the two vectors Ans: 13
b. Calculate the magnitude of the cross product of the two vectors Ans: 7.5
3. Two vectors are given by A = (3.0) i + (1.0) j -(2.0) k and B = (4.0) i +(2.0)j −(3.0) k .
- Find the Magnitude and difference of these two vectors Ans: 7i +3j -5k and -1i -1j +1k
- Calculate the magnitude of these vectors Ans: 3.74 and 5.39
- Calculate the unit vectors for each vector Ans: (3i + 1j -2k)/(3.74) and (4i + 2j -3j)/ (5.38)
- Calculate the dot product of these two vectors (A • B) Ans: 20
- Calculate the cross product of (A X B) Ans: 0i + -1j +2k
- Find the angle between the two vectors Ans: 6.98 degrees
4. A kayaker is attempting to cross a 20m wide river by traveling straight across. The river is flowing at a rate of 5 m/s to the east. The kayaker rows his kayak at a constant speed of 3 m/s.
a. How long will it take the kayaker to cross the river? Ans: 6.67 seconds
b. How far east will the kayaker be of his starting position after he crosses the river? Ans:33.3m
CHALLENGE: An airplane is routed to fly from the Ames airport to the DSM airport (A true course of 184 degrees or 4 degrees west of south). The aircraft has a cruising speed of 130 MPH. The weather reports a steady wind at 15 mph from the west blowing east. What direction must the airplane head (True Heading) in order to fly a direct flight from the Ames airport to the Des Moines Airport? If the distance between the airports is 50 miles, how long will the flight take? Ans: Will be discussed in Thursdays session