Physics

Vandebilt Catholic High School

W. Dupre

Assignment – Solving Vectors Analytically

 

Problems for Regular and Level 1 Classes

  1. Break the following vectors down into their perpendicular components.            a) 500 N at 135°        b) 225 km/hr at 300°   c) 55 mi/hr at 37°
  2. From the x and y components given, find the direction and magnitude of the resultant.    

      a. Fy = 120 N, Fx = 345 N
      b. vy = 31 m/s, vx = 8 m/s
      c. ax = -15 m/s2, ay = 12 m/s2    

  1. A point in the xy plane has cartesian coordinates (- 3.00, 5.00) m. What are the polar coordinates of this point?
  2. A boat makes its way west at 12 m/s, while the current of the river on which it sits is flowing south at a speed of 5 m/s. What is the resultant magnitude and direction of the boat?
  3. If An airplane is flying at 300 miles per hour, heading 30 degrees North of East. What are the magnitudes of the North and East components of the velocity? 

A wind from due North starts blowing at 40 miles per hour. What is the new velocity of the plane? (magnitude and direction)

  1. Three forces act simultaneously on point J. One force is 10.0 N north; the second is 15.0 N west; the third is 15.0 N 300O east of north. Determine the magnitude and direction of the resultant force.

 

Problems for Regular Physics ONLY

 

  1. A soccer ball is kicked with a horizontal velocity of 11.3 m/s and a vertical velocity of 3.5 m/s. What is the magnitude and direction of the ball's velocity?
  2. A hiker leaves camp and, using a compass walks 4 km E, 6 km S, 3 km E, 5 km N, 10 km W, 8 km N, and 3 km S. At the end of three days, the hiker is lost. Determine how far the hiker is from camp and which direction should be taken to get back to camp.
  3. Dan applies a force of 92 N on a heavy box by using a rope held at an angle of 45O with the horizontal. What are the vertical and horizontal components of the 92-N force?
  4. A plane flies at a speed of 250 km/hr North, while being blown by a wind of 75 km/hr West. What will be the plane's resultant speed and direction?

Problems for Level 1 Physics ONLY

 

  1. A ship leaves its home port expecting to travel to a port 500 km due south. Before it can move, a severe storm comes up and blows the ship 100 km due east. How far is the ship from its destination? In what direction must the ship travel to reach its destination?
  2. Kyle is flying a plane due north at 225 km/h as a wind carries it due east at 55 km/h. Find the magnitude and direction of the planes resultant velocity analytically.
  3. A descent vehicle landing on the moon has a vertical velocity toward the surface of the moon of 35 m/s. At the same time, It has a horizontal velocity of 55 m/s. a) At what speed does the vehicle move along its descent path?  B) At what angle with the moon’s surface is this path?
  4. Kyle wishes to fly to a point 450 km due south in 3.00 hours. A wind is blowing from the west at 50 km/hr. Compute the proper heading and speed that Kyle must choose in order to reach his destination on time.
  5. Vector A is 3.00 units in length and points along the positive x axis. Vector B is 4.00 units in length and points along the negative y axis. Use analytical methods to find the magnitude and direction of the vectors (a) A + B, (b) A - B.
  6. A particle moves from a point in the xy plane having cartesian coordinates (- 3.00, - 5.00) m to a point with coordinates (- 1.00, 8.00) m. (a) Write vector expressions for the position vectors in unit-vector form for these two points. (b) What is the displacement vector?
  7. An airplane is flying in the presence of a 100 km/h wind directed due north. What must be the velocity and heading of the plane if it is to maintain a velocity of 500 km/h due east with respect to the ground?