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- 1. a₂ = == A cart is propelled over an xy plane with acceleration components 4.0 m/s² and ay - 3.0 m/s². Its initial velocity has components or =- 6.0 m/s and voy 5 m/s. If the cart passes the origin at t = 1.0s, what are the x and y coordinates of the cart when it reaches its smallest coordinate?In the new model of the pump, water leaves the impeller with a velocity of 25 m/s and an acceleration of 30 m/s², measured relative to the impeller along the blade line AB. The impeller rotates at a constant angular velocity of w = 15 rad/s. B 30° 0.3 m A w = 15 rad/s a) We need to determine the velocity and acceleration of a water particle at point A as it leaves the impeller at the given instant. b) Shallow wells, dug wells, and hand pumps are commonly preferred due to their relatively simple construction and maintenance. Their depth ranges often align with the water requirements of rural communities, serving purposes like domestic use, livestock, and small- scale irrigation. Assist the engineering team in utilizing the provided tables to identify the optimal well type for this pump. Please provide a brief rationale for your choice.A particle P of mass m = 3 kg arrives at point O with a horizontal velocity and starts rolling down a circle with radius R = 1.5 m. The particle is attached to the point O by means of a linear spring of stiffness k = 50 N/m that is unstretched when the particle is at O. Assume that during the motion of P along the circle, the spring follows the circle. Let N = {x, ây} be a fixed reference frame as shown in the figure and let B = {bx, by} be a reference frame attached to P so that b is tangent to the circular path and by is perpendicular to the circular path. For convenience, take g = 10 m/s² in this question. ny ĤT IP
- 4. A stunt plane flying at the Reno Air Races is moving through the sky. The rectangular coordinates describing its motion are: x = -0.74t³ + 2.5t² + 10.25t y = -6.23t² + 16.45t + 8.94 where x and y are given in ft and t is given in seconds. a. Calculate the velocity vector, v, and acceleration, a, of the plane after 10 seconds (velocity is in ft/s and acceleration is in ft/s²). You may want to look back at your Topic 2 notes to recall how position, velocity, and acceleration are related. Your final answer should be given in vector form. b. Calculate the magnitude of the velocity (in mph) and the acceleration (in ft/s²) at t = 10 sec. [Ans. to Check: v = 132.46 mph; a = 41.32 ft/s²]Aeroplane A is flying east at a speed of 600 km/h along the horizontal axis at theinstance shown in the figure below. Aeroplane B passes under A, with its nose pointed45° in the northeast direction. In the meantime, B is moving relatively away from A atan angle of 60° in the direction shown below. a) Draw the vector diagram denoting the relative motion of the aeroplanes. Clearlyannotate each vector to represent velocities of A and B, as well as the velocityof B relative to A. Indicate vector directions using arrows.b) Determine the velocity of B, and the velocity of B relative to A.c) As time progresses from this initial instance, the velocity of aeroplane Aincreases and is defined by v(t) = 4t2 + 2t + 600 km/h. Determine thedisplacement, velocity and acceleration of aeroplane A after 12 seconds.d) Determine the acceleration of B, and the acceleration of B relative to A, at thisnew time instance (t = 12 seconds) as defined in part (c).Q2: The particle P starts from rest at point A at time and changes its speed thereafter at a constant rate of 2g as it follows the horizontal path shown. Calculate the magnitude and direction of its total acceleration for the following: (1) just before point B, (2) just after point B, and (3) As it passes point C. તd PDOW State your directions relative to the x-axis shown (CCW positive). P 3 m B 3.5 m Q
- 6(a) The y-coordinate of a particle in curvilinear motion is given by y = 4.5t3 - 5.9t, where y is in inches and t is in seconds. Also, the particle has an acceleration in the x-direction given by ax = 9.6t in./sec2. If the velocity of the particle in the x-direction is 12.9 in./sec when t = 0, calculate the magnitudes of the velocity v and acceleration a of the particle when t = 1.4 sec. Construct v and a in your solution.A ball (shown in red color) is constrained to move in a circular path and it is also force to move downwards by the slider (shown in blue color) at a constant velocity of 0.5 m/s. Find the magnitude of acceleration of the ball at the instant when 0 = 60°. Show all necessary diagrams. Slider 2 m 0.5 m/sTwo boats leave the shore at the same time and travel in the directions shown. Given that va = 5 m/s and vB = 8 m/s and boat A is increasing it speed at 3m/s? while boat B is decreasing its speed at the rate of 2m/s. a. Find the velocity vector for boat A and B. [2 mark] b. Find the relative velocity vector of boat B with respect to boat A together with its magnitude and direction angle. [3 marks] c. Find the acceleration vector for boat A and boat B [2 marks]. d. Find the relative acceleration vector of boat A with respect to boat B together with its magnitude direction angle. [3 marks]. UB B \30 35°
- 4. The car decelerates uniformly along the curved road from 26 m/s at A to 10 m/s at C. 250 m PB = 300 m, a. What is the car's velocity at B? O b. What is the total acceleration of the car at B? 50 m c. How long will it take the car to travel from A to C?2. Block A (20kg) moved down 2 m in 20 sec starting from rest. Find the final velocity and acceleration of Block B (10kg)n the expression below, i, j, and k are mutually perpendicular unit vectors having directions fixed in a frame of reference. Vector vP is the velocity of point P moving in the frame; t is the time measured in seconds. Determine the acceleration aP at time t = 2 s for the velocity expression given.