Physics

Vandebilt Catholic High School

W. Dupre

Assignment: Vectors

Directions: Solve all problems both graphically & analytically, unless otherwise indicated.

A. Vector Composition on 1 axis. (Solve algebraically)

1. A boat capable of a top speed of 40 mph is traveling downstream along a river that has a current speed of 8 mph. What is the resultant velocity of the boat?
2. If the same boat in problem #1 is traveling upstream, what is the resultant velocity of the boat?
3. A plane traveling with an air speed of 400 mph is traveling into a headwind of 50 mph. What is the resultant ground speed of the plane?
4. A mailman undergoes the following displacements 0.5 km S, 0.8 km N, 1.2 km S, and 0.6 km N. What is his resultant displacement?

B. Vector Composition with 2 perpendicular vectors.

5. An airplane traveling at 18 m/s S is traveling in a crosswind that is blowing 5 m/s W? What is the plane’s resultant velocity?
6. A particle traveling at 65 m/s N is caught in a wind gust blowing 40 m/s E. What is the resultant velocity of the particle?
7. A particle undergoes the following displacements; 4 m W, 7 m N, 8 m E, and 5 m S. What is the resultant displacement of the particle?

C. Vector Composition at any angle. (Regular Classes solve graphically ONLY)

8. A boat traveling 15 m/s 45^O NoW, passes through the gulf stream traveling 8 m/s 10^O NoE. What is the boat’s resultant velocity?
9. A bug undergoes the following displacements; 20 cm E, 12 cm 35^O NoW, and 8 cm S. What is the bug’s resultant velocity?

D. Vector Resolution Problems

10. What are the x and y components of 30 m/s velocity heading 45^O SoE?
11. What are the horizontal and vertical components of a 10 m/s velocity vector oriented 35^O above the horizon?
12. What are the x and y components of a projectile that is fired at an angle of 26^O with the horizon at an initial velocity of 18 m/s?

E. Mixed Problems

13. A boat traveling at 15 m/s at angle 30^O (see diagram) across a river

that is 48 m wide. How many seconds will it take the boat to reach

the other bank? How far downstream will it be from where it originally                  30^O

departed?

14. A boat is rowed at 8 km/h directly across a river that flows at 6 km/h. How fast and in what direction can the boat be rowed to reach a destination directly across the river?
15. (Level 1 only) A skier is accelerating down a 30^O hill at 3.80 m/s^s. What is the vertical component of her acceleration? How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 335m?