Two dogs, Ajax and Bandit, are pulling a Radio Flyer wagon carrying their best cat friend, Casper. the overhead view of the dog force vectors is shown to scale in the grid at the right. (Assume 4 significant figures.) a. Find the single force that is equivalent to the two forces shown. b. If that old rusty wagon DOES NOT MOVE, find the force (including direction) that the ground exerts on the wagon to keep it in place, in spite of the dogs. The forces are measured in units of newtons (N). (You may use EITHER geometry OR vector addition with Cartesian or polar coordinates. Either way, a diagram to scale is required. Be sure to JUSTIFY why your answer to part b is the opposite of your answer to part a.)

Refer to the given figure. Suppose a boat weighs 700 pounds and is on a ramp inclined at 30°. Represent the force due to gravity, F, using F= -700j. Solve, a. Write a unit vector along the ramp in the upward direction. b. Find the vector projection of F onto the unit vector from part (a). c. What is the magnitude of the vector projection in part (b)? What does this represent?

A. Fill in the table completely with the correct answer as required. Picture/Situation Magnitude Direction Scalar or Vector (if none, write NONE) 1. A boy is running at 8 m/s to the north. 2. A box has a mass of 35 kilograms. 3. The length of the table is 2.5 meters. 4. The weight of the student is 500 newtons. B. Determine the resultant vector of the given vectors using graphical method. Connect the given vectors correctly to determine the resultant vector and write your answers on the table. Given vectors Resultant Vector: (V1+ V2) V1 V2 Using Polygon Method Using Parallelogram Method C. Draw or locate properly the following vector directions in the given Cartesian plane. Use protractor to measure the angle. A. 40 north of east 59 south of west 15 south of east D. 30° west of north D. A student runs initially at 3 m/s to the north, and suddenly accelerates at 4 m/s to the East. Find his resultant velocity (magnitude and direction). Show all your solution.

Two force vectors are added together. The vectors are as follows. Vector A is a force of 52 Newton’s at an angle of 62 degrees. This angle is measured up from the horizontal toward the right Vector B is a force of 120 Newton’s at an angle of 58 degrees. This angle is measured up from the horizontal toward the left. A. What is the magnitude of the net force? (In Newton’s)? B.Find the direction (angle) of the net force as measured up from the horizontal?