Determine the vector magnitudes and directions for the relative velocities VA/B and VB/A, given these magnitudes and directions for the vectors VA and VB: (a) VA: magnitude 70km/h; direction 30⁰ VB: magnitude 50km/h; direction 125°
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- 4. The slider travels along the guide rod AB with the velocity v= 28 ft/s. Determine the vector component representations of the unit vector directed from A toward B; and the velocity vector v. 16 m В 8 m 12 m 10 m4 Problem Consider two cars A and B moving at constant speeds VA = 60 kph and VB = 80 kph. Car A is traveling along a circular road that has radius r = 300 meters and is at an angle of 0 = 45 deg relative to car B. Car B is traveling westbound along a straight line. A VA r UB A B Determine a symbolic expression for (a) the relative velocity vector A/B using the unit vectors of a polar reference frame defined at point B, (b) the angular rate è, and (c) the radial rate r. Numerically evaluate your expressions for and r. (Hint: Begin by expression both VA/O and VB/O in terms of polar frame unit vectors.)A camera on the left edge of a circular track of radius D = 4 m tracks a particle as it travels around the circle. The polar equation of the path is given above. At the moment shown, the camera angle is € = 30°, and the camera is rotating at 0 = 0.5 rad/s, which is accelerating at a rate 0 -0.1 rad/s². What is the velocity, acceleration, and rate of change of speed of the particle at that instant? = V= r = D cos(0) a = v = m/s m/s² m/s²
- The slider travels along the guide rod AB with the velocity v= 8 m/g.Determine the rectangular representations of (a) the unit vector directedfrom A toward B; and (b) the velocity vector v.Vr A camera tracks the position of a particle moving along the given path with b = 10 m. At the moment shown, the camera angle is 0 = 40°, and the camera is rotating at 0.3 rad/s, which is accelerating at a rate 0 = 0.2 rad/s². What are the radial and transverse components of velocity and acceleration at this instant? Vo = Ar 0 ao = r = b sin(20) m/s m/s m/s² m/s² =4. 3) The hydraulic cylinder D extends, moves the rigid rod ABC, and causes the collar A to move with velocity and acceleration both to the left. If the dimensions 4 = 1.0 ft, and 2 = 1.6 ft, VA = 3.6 ft/s, aa = 2.2 ft/s2, and the angle 0 = 27°, determine the speed of point C. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper unit. %3D В 12 D Your Answer: Answer units 1,
- find the center of mass, the velocity of the center of mass, the momentum, and the kinetic energy of the following system: m₁ = 1 kg T₁=1+2+3 k v₁ = 2î + 3ĵ m₂ = 1 kg T₂ = î -Ĵ+ k v₂ = 2ĵ + 3k3. Consider the conveyor belt shown below. As the rollers turn at a constant rate, the top portion of the belt moves to the right at speed v. D- -B Lêu E Assuming the belt does not stretch, answer the following sub-questions. Express your answers in terms of basis vectors (ê1, ê2). (a) What is the velocity vector of point A on the belt? Why? (b) What is the velocity vector of point C of the belt? Why? (c) What is the velocity vector of point B of the belt? Why? (d) What is the velocity vector of point E at the center of one of the rollers? Why? (e) What is the velocity vector ic/a? (f) What is the velocity vector Ta/c? (g) What is the velocity vector &B/A? (h) What is the velocity vector ve/c? (i) What is the velocity vector A/E?1. Two mobile containers, A and B, carries raw materials for concrete batching plant. The containers' motions are defined by their velocity vectors: for container A, A = 6i + 4k (km/hr) and for container B, B = -4i +7k (km/hr). What is the angle between the line of action (path) of both containers? Express your answer in units of degree. 2. Two cables A and B are attached to a hook. Cable A exerts a pull with a magnitude and direction defined by the vector A = 6i + 4k (kN). Cable B is also attached to the same hook where cable A is attached, cable B exerts a pull with a magnitude and direction defined by the equation B = -4i +7k (kN). What should be the magnitude of pull exerted at cable B such that the line of action of resultant force is along the positive z-direction (the resultant lies along the positive z-axis)? Express your answer in unit of kN.
- A sailboat race course consists of four legs, defined by displacement vectors A, B, C and D. The magnitudes of the first three vectors are A=3.0km, B=5.50km, and C=4.50km. The finish line of the course coincides with the starting line. What is the distance of the fourth leg and the Angle.The wheel rolls on the conveyor belt without slipping. The velocity of the centre O of the wheel s 1.83 m/s to the left, whereas the conveyor is moving to the right at 1.22 m/s. Determine the angular velocity of the wheel.Obtain the equations of motion governing this system