**Unit 7: Vectors and
Projectiles**

**Problem Set B**

The following selection of problems are sample problems. Individual student problem sets will vary since numerical information is randomly-generated.

**Directions:**

For the following problems:

- compute the unknown quantity and enter the answer in the blank.
- give regard to positive and negative values and include the sign in the answer (if negative).
- do not round any computed numbers until the last calculation.
- enter your answers accurate to the second decimal place (unless told otherwise).

**Problem 1: **

The two displacement vectors A and B have a magnitude of 2.98 m. Vector A has a direction of 108 degrees. Vector B has a direction of 211 degrees. Find the magnitude (in meters) of A + B using component analysis.

**Problem 2:**

(Referring to the previous problem.) Use component analysis to determine the magnitude (in meters) of A - B.

**Problem
3: **

A person going for a walk follows the path shown in the unscaled diagram at the right (Figure 3.18). The total trip consists of four straight- line paths. The magnitude of the individual displacements are: A = 88 m; B = 272 m; C = 136 m; D = 183 m. At the end of the walk, what is the person's resultant displacement (in meters) measured from the starting point?

**Problem 4: **

An airplane flies from city A to B in a direction due east for 732 miles. In the next part of the trip the airplane flies from city B to city C in a direction 35.5 degrees north of east for 514 miles. What is the magnitude (in miles) of the resultant displacement of the airplane between city A and city C?

**Problem 5: **

(Referring to the previous problem.) What is the direction (in degrees) of the resultant displacement of the airplane? Use the counter-clockwise from east convention.

**Problem 6: **

While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 68 m north, 246 m east, 112 m at an angle 30 degrees north of east, and 159 m south. Find the magnitude of the resultant displacement (in meters) from the cave entrance.

**Problem 7: **

(Referring to the previous problem.) What is the direction (in degrees) of the resultant displacement? Use the counter-clockwise from east convention.

**Problem 8: **

An airplane begins its journey into Canada from a destination located 285 mi south of the border. The plane flies along a straight-line path at 189 mi/h in a direction of 20.5 degrees west of north. Determine the number of minutes before the plane crosses the border.

**Problem 9: **

An escalator is 18.5 m long. If a person stands on the 'up' side, it takes 50.9 s to ride to the top. If a person walks up the moving escalator with a speed of 0.505 m/s relative to the escalator, how long (in seconds) does it take to the get to the top?

**Problem 10: **

(Referring to the previous problem.) If a person walks down the 'up' escalator with the same relative speed as in the previous problem, how long (in seconds) does it take to reach the bottom.

**Problem 11: **

A boat moves at 4.9 m/s relative to the water regardless of which direction it travels through the water. If the water in a river is flowing at 1.5 m/s, how long (in seconds) does it take the boat to make a round trip consisting of a 285 m displacement downstream followed by a 285 m displacement upstream.

**Problem 12: **

A river flows due east at 2.5 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 7.3 m/s due north relative to shore. What is the magnitude of the velocity of the boat (in m/s) relative to the shore?

**Problem 13: **

(Referring to the previous problem.) If the river is 242 m wide and the boat heads directly across it, then how much time (in seconds) does it take the boat to reach the opposite shore?

**Problem 14: **

(Referring to the previous problem.) If the river is 242 m wide and the boat heads directly across it, then how far downstream (in meters) has the boat moved by the time it reaches the North shore?

**Problem 15: **

The pilot of an aircraft wishes to fly due west in a wind blowing at 45 km/h toward the south. If the speed of the aircraft in the absence of wind is 165 km/h, in what direction (in degrees) should the aircraft head? Use the counter-clockwise from east convention.

**Problem 16: **

(Referring to the previous problem.) What will be the airplane's speed (in km/h) relative to the ground?

**Problem 17: **

Two canoeists in identical canoes exert the same effort paddling and hence maintain the same speed relative to the water. One paddles directly upstream (and moves upstream), whereas the other paddles directly downstream. Downstream is the positive direction. An observer on shore determines the velocities of the two canoes to be -1.02 m/s and +2.56 m/s respectively. What is the speed of the water (in m/s) relative to shore? Enter a + number. Enter your answer to the third decimal place.

**Problem 18: **

A boat heads due east directly across a 117-m wide river. The water flows due south with a speed of 2.1 m/s with respect to the shore. The boat speed with respect to the water is 2.9 m/s. Determine the magnitude of the velocity (in m/s) with respect to the shore.

**Problem 19: **

(Referring to the previous problem.) Determine the direction (in degrees) of the velocity with respect to the shore. Use the counter-clockwise from east convention.

**Problem 20: **

(Referring to the previous problem.) Determine the distance (in m) that the boat will have traveled downstream when it has reached the opposite shore.

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