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A satellite will travel indefinitely in a circular orbit around the earth if the normal component of its acceleration is equal to
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Vector Mechanics For Engineers
- The motion of a particle is defined by the function x = at3 - bt2 - ct + d where x is in centimeters and t is in seconds When is the particle at rest if a = 1.3, b = 3.5, c = 8.3, and d = 5.2?arrow_forwardA group of students launches a model rocket in the vertical direction. Based on tracking data, they determine that the altitude of the rocket was 89.6 ft at the end of the powered portion of the flight and that the rocket landed 18.5 s later. The descent parachute failed to deploy so that the rocket fell freely to the ground after reaching its maximum altitude. Assume that g = 32.2 ft/s2. Determine the speed v1 of the rocket at the end of powered flight. The speed is ____ ft/s.arrow_forwardThe path of motion of a 5-lb particle in the horizontal plane is described in terms of polar coordinates as r = (2t + 1) ft and u = (0.5t2 - t) rad, where t is in seconds. Determine the magnitude of the unbalanced force acting on the particle when t = 2 s.arrow_forward
- A 180-lb man and a 120-lb woman stand side by side at both ends of the 300-lb boat, ready to dive, each with a 16-ft/s speed relative to the boat. Determine the speed of the boat after they both dive, if (a) the woman dives first, (b) the man dives first. (show your solution) choices of correct answer: 3.0723 km/hr ; 0.251 km/hr 13.0723 km/hr ;1.251 km/hr 10.095 km/hr; 10.2815 km/hr 18.0723 km/hr; 0.521 km/hr 0.251 km/hr; 8.0723 km/hrarrow_forwardA car that is initially at rest accelerates along a straight, level road according to the diagram shown. Determine (a) the maximum speed; and (b) the distance traveled by the car when the maximum speed is reached.arrow_forwardAn airplane has a mass of 25 Mg and its engines develop a total thrust of 40 kN during take-off. If the drag D exerted on the plane has a magnitude D= 2.25 v2, where is expressed in meters per second and D in newtons, and if the plane becomes airborne at a speed of 240 km/h, determine the length of runway required for the plane to take off.arrow_forward
- A 1400-kg automobile starts from rest and travels 400 m during a performance test. The motion of the automobile is defined by the relation a= 3.6e-0.0005 x, where a and x are expressed in m/s2 and meters, respectively. The magnitude of the aerodynamic drag is D = 0.35v2 , where D and v are expressed in newtons and m/s, respectively. Determine the power dissipated by the aerodynamic drag when (a) x = 200 m, (b) x = 400 m.arrow_forward2- Each ball has a negligible size and a mass of 5 kg and is attached to the end of a rod whose mass may be neglecte. If the rod is subjected to a torque M=t2+2) N.m. where tis in seconds, determine the speed of each ball when t = 2 s. Each ball has a speed v = 4m / s when t = 0 .arrow_forwardBall A is released from rest at height 85m at the same time that a second ball B is thrown upward from a distance 2m above the ground. If the balls pass one another at a height 25m.(a) Determine the speed at which ballB was thrown upward. (b) Determine the speed of ball Bwhen the balls pass one another (c) Determine the total time of travel when the balls pass one another. acceleration due to gravity = 9.81m/s2arrow_forward
- Car A starts from rest at t =0 and travels along a straight road with a constant acceleration of 8 ft/s2 until it reaches a speed of 80 ft/s. Afterwards it maintains this speed. Also, when t =0, car B located 8000 ft down the road is traveling towards car A at a constant speed of 60 ft/s. Determine the distance travelled by car A when they pass each other. A.3,600 ft B.4,400 ft C. 5,600 ft D. None of thesearrow_forwardIn anticipation of a long 7° upgrade, a bus driver accelerates at a constant rate of 3 ft/s2 while still on a level section of the highway. Knowing that the speed of the bus is 60 mi/h as it begins to climb the grade and that the driver does not change the setting of his throttle or shift gears, determine the distance traveled by the bus up the grade when its speed has decreased to 50 mi/h.arrow_forwardPrinciple of Angular Impulse and Momentum To apply the principle of angular impulse and momentum to find final speed and the time to reach a given speed. As shown, ball B, having a mass of 10.0 kg, is attached to the end of a rod whose mass can be neglected. Finding the final speed of the ball If the rod is 0.550 m long and subjected to a torque M=(1.95t2+3.75) N⋅m, where t is in seconds, determine the speed of the ball when t=4.80 s. The ball has a speed of v=2.25 m/s when t=0 Finding the time needed to reach a specific speed If the shaft is 0.250 m long, the ball has a speed of v=2.85 m/s when t=0, and the rod is subjected to a torque M=(3.40t+2.15) N⋅m, where t is in seconds, determine the time it will take for the ball to reach a speed of 5.80 m/s.arrow_forward
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