Question

Please show work

Your group should discuss and solve all problems below. Each student in the group should prepare a neat solution to ONE of the 4 problems (different problems for each group member) Consider the two vectors A and B having directions as shown in the fi 0Al A 61 units) and the magnitude of B is 55 un55 units) 1. gure. The magnitude of A is 61 units ㄩ 52" B68 (a) Write an expression for each vector using unit vector notation [For example, A-A,itA (b) If the two vectors are added together, they give a vector sum (or resultant) R-A+B for K using unit vector notation. Write an expression (c) Express R in polar vector notation in terms of magnitude and direction 2. Sam is travelling in his car down Broad Street at 21 m/s. When Sam is 59 m from a traffic light it turns yellow Sam instantly steps on the gas and accelerates toward the intersection (constant . Sam passes under the traffic light 2.5 seconds later just as the light turns red. a) Choose a coordinate system and identify the given parameters. b) Use an equation of motion to find Sam's acceleration. c What was Sam's velocity as he passed under the traffic light? 3. A car traveling at a constant 39 m/s (87 mph) passes a police car that is initially traveling at 25 m/s (55 mph). At the instant of the pass, the police car accelerates at a constant rate of 3.3 m/s in pursuit. We wish to find how much time elapses before the officer catches the car (a) Identify the initial states when the car passes the police (b) Define the final state or conditions which enable you to answer the above question. (c) To solve this problem identify the two equations (one for each vehicle) which satisfy part b. Solve for the time.

Answer 1

A^vector = 61 units at 52 degrees with - x or 128 degrees with tx in ccw A^vector = 61 cos(128 degrees) i^dot + 61 sin (128 degrees)j^dot A^vector = -37.56 i^dot + 48.07j^dot B^vector = 55 units at theta = 270 degrees - 68 degrees with + x in ccw theta = 202 degrees B^vector = 55 cos 202 degrees i^^+ 55 sin 202 degrees j^dot B^vector = -51.00 i^dot - 20.60 j^dot R^vector = A^vector + B^vector - 37.56 i^dot + 48.07 j^dot + (-51.00i^dot - 20.60 j^dot) R^vector = -88.56 i^dot + 27.47 j^dot c) The magnitude implies R = squareroot 88.56^2 + 27.47^2 R = 92.72 direction: - theta = tan^-1(R y/Rx) theta = tan^-1(27.47/-88.56) Direction theta = 162.77 degrees with +x in ccw choosing x = 0 when he starts to accelerate V_i = initial velocity = 21 m/s, x_i = 0m acceleration implies a distance from intersection = d = 59m time(t) to reach traffic light