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- 4) Two vectors have equal magnitudes of 2.0 m. Find graphically the angle between them if the magnitude of their resultant is (a) 3.0 m; (b) 1.0 m. In each case use the law of cosines to confirm your answer. Problems 3 and 4 are graphical solutions. Please use a protractor, ruler, and compass and work as accurately as possible. Alternatively, you could use a vector drawing program to work out the geometry1. Let v = -51 + 53 be a vector in R². (a) Find v. (b) Find the angle, 0, in degrees, that v makes with the positive x-axis. (Answer in radians between 0 and 27.) (c) Find a unit vector that points in the same direction as v. Answer in component form.a. The two parallel lines (1, m) drawn below ate intersected by a third line. If angle 1 is 20 degrees, what are the values of the other angles 2, 3, 4, 5, 6, 7? 4 7/2 5 6 b. Given the geometry shown below, what is the value of the angle a? α 35° 00
- Two points are given in polar coordinates by (r, 8) = (1.20 m, 50.0°) and (r, 0) = (4.00 m, -42.0°), respectively. What is the distance between them? m5:02 94%| This is a diagram of the earth and something or someone standing. The figure is rotated so that the person or object is at the top. The object is not to scale compared with the earth. In fact, the object (height h) is far smaller than the radius of the earth. We will calculate the distance and angle viewable at the top of the arrow. h R To start with, calculate h/R * 100000, given the following numbers. (Multiplying by some large number is the only way to get a non-zero answer out of the computer.) •h = 6*10? meters R 6.37 * 106 meters %D1. Draw and label the vector with these components. Then determine the magnitu angle of the vector. a- A, = 3 ,Ay = -2 b- By = -2 ,By = 2 2. What is the speed of horse in meter per second that runs a distance of 1.2 miles- minutes? 3. A car moving along X- axis according on the function: X (t) = 2 t² + 5 t +7 on [1,2] Find: a- The average velocity. b- The acceleration at 3s. 4. Julie is walking around a track at a 2m/s for some exercise. She then decides t gging so she accelerates at a rate of 0.5m/s² for 3 seconds. ow far did Julie travel from the time she started to accelerate to the end of the 3 seco 5. Ralph uses a 2000 N force to push his car along a road for 1000 m. It takes hin to do this. a- Calculate the amount of work that Ralph did on the car. b- Calculate the amount of power that he generated.