A 20-kg base satellite deploys three sub-satellites, each of which has its own thrust capabilities, to perform research on tether propulsion. The masses of sub-satellites A, B, and C are 4 kg, 6 kg, and 8 kg, respectively, and their velocities expressed in m/s are given by
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Vector Mechanics For Engineers
- The 18 000-kg F-35B uses thrust vectoring to allow it to take off vertically. In one maneuver, the pilot reaches the top of her static hover at 200 m. The combined thrust and lift force on the airplane applied at the end of the static hover can be expressed as F = (44t + 2500t2)i + (250t2 + t + 176 580)j, where F and t are expressed in newtons and seconds, respectively. Determine how long it will take the airplane to reach a cruising speed of 1000 km/hr (cruising speed is defined to be in the x-direction only).arrow_forwardAn airline employee tosses two suitcases with weights of 30 lb and 40 lb, respectively, onto a 50-lb baggage carrier in rapid succession. Knowing that the carrier is initially at rest and that the employee imparts a 9-ft/s horizontal velocity to the 30-lb suitcase and a 6-ft/s horizontal velocity to the 40-lb suitcase, determine the final velocity of the baggage carrier if the first suitcase tossed onto the carrier is (a) the 30-lb suitcase, (b) the 40-lb suitcase.arrow_forwardA 1400-kg automobile starts from rest and travels 400 m during a performance test. The motion of the automobile is defined by the relation x= 4000 ln(cosh 0.03t), where x and t are expressed in meters and seconds, 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) t= 10 s, (b) t= 15 s.arrow_forward
- at an amusement park there are 200 kg bumper cars A, B, and C that have riders with masses of 40kg, 60 kg, and 35 kg, respectively. Car A is moving to the right with a velocity Va=2m/s when it hits stationary car B. The coefficient of restitution between each car is 0.8. Determine the velocity of car C so that after car B collides with car C the velocity of car B is zero.arrow_forwardA pile-driver of mass 500 kg falls freely through a height of 1.5 m on to a pile of mass 200 kg. Determine the velocity with which the driver hits the pile. If, at impact, 3 kJ of energy are lost due to heat and sound, the remaining energy being possessed by the pile and driver as they are driven together into the ground a distance of 200 mm, determine (a) the common velocity immediately after impact, (b) the average resistance of the ground.arrow_forwardA billiard player sends the cue ball toward a group of three balls that are initially at rest and in contact with one another. After the cue ball strikes the group, the four balls scatter, each traveling in a different direction with different speeds as shown in the figure below. If each ball has the same mass, 0.16 kg, determine the total momentum of the system consisting of the four balls immediately after the collision. (Assume v1 = 0.33 m/s, θ1 = 70°, v2 = 0.49 m/s, θ2 = 30°, v3 = 0.21 m/s, v4 = 0.48 m/s.) magnitude ? (in kg m/s^2) direction ? (in degrees counterclockwise from the + x-axis)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_forwardA rocket weighs 2600 lb, including 2200 lb of fuel, which is consumed at the rate of 25 lb/s and ejected with a relative velocity of 13,000 ft/s. Knowing that the rocket is fired vertically from the ground, determine (a) its acceleration as it is fired, (b) its acceleration as the last particle of fuel is being consumed, (c) the altitude at which all the fuel has been consumed, (d) the velocity of the rocket at that time.arrow_forwardA 35 000-Mg ocean liner has an initial velocity of 4 km/h. Neglecting the frictional resistance of the water, determine the time required to bring the liner to rest by using a single tugboat that exerts a constant force of 150 kN.arrow_forward
- A 20-kg base satellite deploys three sub-satellites, each which has its own thrust capabilities, to perform research on tether propulsion. The masses of sub-satellites A, B, and C are 4 kg, 6 kg, and 8 kg, respectively, and their velocities expressed in m/s are given by vA = 4i - 2j +2k, vB = i + 4j, vC = 2i + 2j +4k. At the instant shown, what is the angular momentum HO of the system about the base satellite?arrow_forwardTo use the principle of work and energy to determine characteristics of a system of particles, including final velocities and positions. The two blocks shown have masses of mA = 56 kg and mB = 74 kg . The coefficient of kinetic friction between block A and the inclined plane is μk = 0.15 . The angle of the inclined plane is given by θ = 40 ∘ . Neglect the weight of the rope and pulley. Determine the magnitude of the normal force acting on block A, NA If both blocks are released from rest, determine the velocity of block B when it has moved through a distance of s = 2.00 m. If both blocks are released from rest, determine how far block A has moved up the incline when the velocity of block B is (vB)2 = 6.25 m/s.arrow_forwardA 400-kg satellite was placed in a circular orbit 1500 km above the surface of the earth . At this elevation the acceleration of gravity is 6.43 m/s^2. Determine the kinetic energy of the satellite in kJ, knowing that its orbital speed is 25.6*10^ 3 km/h .arrow_forward
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