Physics 11

WS 7.3 - Applications of Vectors

 

The Across the River Problem

 

1.   A boat can travel 2.30 m/s in still water. If the boat heads directly across a river with a current of 1.50 m/s:

  1. What is the velocity of the boat relative to the shore?                       2.75 m/s
  2. At what angle compared to straight across is it traveling?                 q  = 33.1˚
  3. How far from its point of origin is the boat after 8.0 s?                     22 m
  4. At what upstream angle (compared to straight across) must the boat travel in order to the other bank directly opposite its starting point? How fast across the stream is it traveling?              q = 40.7˚, 1.74 m/s

 

Vector Problems (Trig. Solutions)

 

1.     How far East has a person walked if he travels 350 m in a direction 25° E of N?                 148 m

2.     What would be the resulting displacement if a snail crawls 2.0 m north and then 3.0 m east? What is the snail's direction from the starting point?          3.6 m & 33.7˚ N of E

3.     Find the magnitude and direction from the horizontal of a 40.0 N upward force and 17.0 N horizontal force.                                                                43.5 N at 67˚

4.     A boat travels east at 13 km/hr when a tide is flowing north at 1.2 m/s. Find the actual velocity and heading of the boat.                                      3.8 m/s at 18.4˚ N of E

5.     A person that swims at 3.2 m/s swims straight across a river with a current of 1.4 m/s. What is the resulting velocity of the swimmer (across and down stream)? At what angle compared to straight across is the swimmer moving?         3.5 m/s at 23.6˚

6.     The swimmer above decides to swim into the current at such an angle that he will travel straight across.  Find the angle (compared to straight across) at which he would have to swim. Calculate the velocity across the stream.              2.9 m/s at 25.9˚

 

Vector problems (Component or Sine-Cosine Law Solutions)

 

1.     A seagull flying with an air speed of 10.0 km/h is flying north but suddenly encounters a wind of 5.0 km/h at 20° south of east. What will be the new direction and airspeed of the seagull? 9.5 km/h at 60.5˚ N of E

2.     A pilot wishes to reach a city 600.0 km away in a direction of 15° S of W in two hours. (v = 300 km/h at this same direction - this is the resultant vector in the vector diagram!) If there is a wind of 70 km/h blowing at 10° W of S. What must be the heading and air speed of the plane? heading is 2˚ S of W at an airspeed of 278 km/h

3.     A plane that can fly at 250 km/h wishes to reach an airport that has a bearing of 25° W of N from its present location. If there is a 50.0 km/h wind blowing directly to the west what should be the heading of the plane. 14.6˚ W of N (set up vector diagram and then use Sine Law) What will be its ground speed? 267 km/h How long would it take to get to the airport if it were 560 km away? 2.1 hours