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A girl operates a radio-controlled model car in a vacant parking lot. The girl's position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the x-y plane. The motion of the car is defined by the position
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Vector Mechanics For Engineers
- The spatial motion of a particle is described by? = 3? 2 + 4? ? = −4? 2 + 3? ? = −6? + 9where the coordinates are measured in feet and the time t is in seconds. (a) Determine the velocity and acceleration vectors of the particle as functions of time. (b) Verify that the particle is undergoing plane motion (the motion is not in a coordinate plane) by showing that the unit vector perpendicular to the plane formed by v and a is constant.arrow_forwardSome asteroid is moving towards a base in space, such that the base is positioned on the xaxis and is 2000 meters wide on the xaxis. This asteroid, moving at 500 m/s along the yaxis, is on a collision course targeted at the center of the base. However, explosives are planted on the asteroid, which makes it explode into two separate pieces. The two separate pieces of a mass of m and 2m. 1. Please draw the trajectory of the CM of the asteroid as well as the system after the explosion (with the two separate masses). 2. At the same time, the two split pieces of asteroid reach the base. The piece with mass, m, passes by the right side of the bass at 1800m from the edge of the bass. Will the asteroid piece with mass, 2m, hit the base? Please prove if it will or will not. 3. The asteroid piece of mass, m, will be moving at a direction that is makes a 30 degree angle along the x axis, and its speed will be 1000 m/s. What is the speed of the split asteroid of mass, 2m?arrow_forwardAn accelerometer record for the motion of a given part of a mechanism is approximated by an arc of a parabola for 0.2 s and a straight line for the next 0.2 s as shown in the figure. Knowing that v = 0 when t= 0 and x= 0.8 ft when t= 0.4 s, (a) construct the v-t curve for 0 ≤ t≤ 0.4 s, (b) determine the position of the part at t= 0.3 s and t= 0.2 s.arrow_forward
- The trajectory of a soccer ball is analyzed when a goalkeeper decides to place it in the center of the field. Theball is kicked at a height of 1.20 meters measured from the ground with a direction of 25 degrees withrelative to the vertical. It was observed through cameras that the ball remained in the air for 2.4seconds. Determine:a- The speed with which the ball goes out.b- The hot horizontal distance it travels before hitting the ground.c- The maximum height the ball reaches.arrow_forwardCar A is traveling at a constant speed of vA = 130 kph at a location where the speed limit is 100 kph. The police officer in car P observes this speed via radar. As Car A passes P, the car uniformly decelerates to the speed limit for 5 seconds and maintained the motion. Meanwhile, the police car begins to accelerate at the constant rate of 6 m/s2 until a velocity of 160 kph is achieved, and that speed is maintained. Determine the deceleration of car A to reach the speed limit,What is the distance traveled by the police to overtake car A, How long did it take for the police officer to overtake car A?arrow_forwardTo study the performance of a race car, a high-speed camera is positioned at point A. The camera is mounted on a mechanism which permits it to record the motion of the car as the car travels on straightaway BC. It took 0.5 s for the car to travel from the position θ = 60° to the position θ = 35°. Knowing that b = 24 m, determine the average speed of the car during the 0.5-s interval. The average speed of the car during the 0.5-s interval is ______ km/h.arrow_forward
- -Car A moving at a constant velocity of 25 m/sec passes a gasoline station. At the same instant, car B leaves the same gasoline station and travels the same direction as that of car A. Determine the required acceleration of car B in order to overtake car A after 35 seconds. -Two cars A and B are travelling in the same direction with a velocity of 30 m/sec. Car A is 250 meters behind car B. After 17 seconds, car B decelerates at a constant rate. Determine the deceleration of car B so that car A can overtake after 17 seconds.arrow_forward1. In this type of motion, the acceleration “a” of the particle is zero for every value of “t”.2. When a particle P is moving to a position P’ with their corresponding change in radius of curvature and change in the arc length respectively with respect to the origin, the motion is simply define as?3. This component of the particle was shown to be equal to the time derivative of the position coordinate x.arrow_forwardDynamics of Rigid Bodies - Mechanical Engineering A particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x = 6.0t^2 - 6.7t and y = 1.3t^2-t^3/5.5. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors make with the x-axis when t = 3.3 s. Subject: Mechanical Engineeringarrow_forward
- A particle, originally at rest and located at point (3 ft,2 ft, 5 ft), is subjected to an acceleration a = {6ti + 12t^2k} ft/s^2. Determine the particle’s position (x, y, z) when t = 2 s.arrow_forwardA ball is suspended from a light 1.4 m string as shown. The string makes an angle of 28 degrees with the vertical. The ball is then kicked up and to the right such that the string remains taut the entire time the ball swings upwards. This kick gives the ball an initial velocity of 1.1 m/s. What will be the speed, in meters per second, of the ball when it reaches its lowest point (θ = 0)? What will be the maximum angle, in degrees, the string will make with the vertical?arrow_forwardA car moved on a horizontal path from rest at constant acceleration from point A until it reached its maximum speed when passing by At point b it took 4 seconds, and after point B it continued its movement but at a slowdown of -3 m / s2 until it stopped at c Categorical The idling distance of 13.5 m. Find: 1. The distance the car traveled while accelerating from a to b 2. The car's rate of acceleration (acceleration) 3. The car's maximum speed from point b 4. The time the car took when slowing down from b to carrow_forward
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