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The parasailing system shown uses a winch to pull the rider in toward the boat, which is traveling with a constant velocity. During the interval when
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Vector Mechanics For Engineers
- The horizontal motion of the plunger and shaft is arrested by the resistance of the attached disk which moves through the oil bath. The velocity of the plunger is v0 = 3.8 m/s in the position A where x = 0 and t = 0, and the deceleration is proportional to v so that a = -kv where k = 0.61 s-1. Find (a) the velocity when t = 5.5 s, (b) the position x when t = 5.5 s, (c) the velocity when x = 3.5 m.arrow_forwardA helicopter starts from rest at point A and travels along the straight-line path with a constant acceleration a. If the speed v = 33 m/s when the altitude of the helicopter is h = 40 m, determine the values of r˙, r¨, θ˙, and θ¨ as measured by the tracking device at O. At this instant, θ = 34°, and the distance d = 185 m. Neglect the small height of the tracking device above the ground.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_forward
- A motorcycle starts from rest at t = 0 and travels along a straight road with a constant acceleration of 6 ft/sec2 until it reaches a speed of 50 ft/s and maintains this speed throughout the duration of the motion. Also, when t = 0, a car located 6000 ft away, travels towards the motorcycle at a constant velocity of 30 ft/s. Determine the time at which the two vehicles pass each other,Calculate the distance traveled by the motorcycle the moment that the two vehicles pass each other, Calculate the distance traveled by the car the moment that the two vehicles pass each other.arrow_forwardAn engine driver suddenly puts on his brake and shuts off steam when he is running at full speed; in the first second afterwards the train travels 28 m and in the next second 26 m. Find (i) the original speed of the train, (ii) the time before it comes to rest, (iii) the distance it will travel in that interval, assuming the brake to cause a constant retardation. Find also the time the train will take, if it be 30 m long, to pass a spectator standing at a point 150 m ahead of the train at the instant when the brake was applied.arrow_forwardThe curvilinear motion of a particle is defined by vx = 50− 16t and y = 100 − 4t2, where vx is in meters per second, y is in meters, and t is in seconds. It is also known that x = 0 when t = 0. Plot thepath of the particle and determine its velocity and acceleration when the position y = 0 is reached.arrow_forward
- In both cases a spaceship is pulling two cargo pods, one empty and one full. At the instant shown, the speed of the pods and spaceships is 300 m/s, but they have different accelerations as shown. All masses are given in terms of M, the mass of an empty pod. a) b)arrow_forwardA subway car leaves station A; it gains speed at the rate of 4 ft/s² for 6 s and then at the rate of 6 ft/s² until it has reached the speed of 48 ft/s. The car maintains the same speed until it approaches station B; brakes are then applied, giving the car a constant deceleration and bringing it to a stop in 6 s. The total running time from A to B is 40 s. Determine the distance between stations A and B. . Do not type the solution. Show the complete computation/solution with the necessary graphs or diagrams.arrow_forwardCar A is traveling at the constant speed of 58 km/h as it rounds the circular curve of 350-m radius and at the instant represented is at the position θ = 42°. Car B is traveling at the constant speed of 69 km/h and passes the center of the circle at this same instant. Car A is located with respect to car B by polar coordinates r and θ with the pole moving with B. For this instant determine vA/B and the values of r˙ and θ˙ as measured by an observer in car B. Write vA/B in terms of the polar coordinates. Answer: vA/B = ( ___ er +____ eθ) m/sarrow_forward
- The motion of a vibrating particle is defined by the position vector r= (4 sin πt) i- (cos 2πt)j, where r is expressed in inches and t in seconds. (a ) Determine the velocity and acceleration when t = 1 s. (b) Show that the path of the particle is parabolic.arrow_forwardCar A is traveling at the constant speed of 58 km/h as it rounds the circular curve of 350-m radius and at the instant represented is at the position θ = 42°. Car B is traveling at the constant speed of 69 km/h and passes the center of the circle at this same instant. Car A is located with respect to car B by polar coordinates r and θ with the pole moving with B. For this instant determine vA/B and the values of r˙ and θ˙ as measured by an observer in car B. For this instant determine the values of r˙ and θ˙ as measured by an observer in car B.Answers: r˙ = m/s θ˙ = rad/sarrow_forwardA loaded railroad car is rolling at a constant velocity when it couples with a spring and dashpot bumper system. After the coupling, the motion of the car is defined by the relation x = 60e - 4.8t sin 16t, where x and t are expressed in millimeters and seconds, respectively. Determine the position, the velocity, and the acceleration of the railroad car when (a) t= 0, (b) t = 0.3 s.arrow_forward
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