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In a water-tank test involving the launching of a small model boat, the model's initial horizontal velocity is 6 m/s and its horizontal acceleration varies linearly from -12 m/s2 at
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- Human centrifuges are often used to simulate different acceleration levels for pilots. When aerospace physiologists say that a pilot is pulling 9 g,s , they mean that the resultant normal force on the pilot from the bottom of the seat is nine times their weight. Knowing that the centrifuge starts from rest and has a constant angular acceleration of 1.5 RPM per second until the pilot is pulling 9 g's and then continues with a constant angular velocity, determine (a) how long it will take for the pilot to reach 9 g's (b) the angle 0 of the normal force once the pilot reaches 9 g’s. Assume that the force parallel to the seat is zero.arrow_forwardA motorboat and its load weigh 980 kg. Assume that the propeller force is constant and equal to 24 kg, and the water resistance is numerically equal to 1.5v kg, where v is the speed at any instant time in m/sec. If the boat starts from rest, determine its speed at the end of 10 seconds. Answer is 2.23 m/sarrow_forwardA motorboat and its load weigh 2150 N. Assume that the propeller force is constant and equal to 110N, and the water resistance is numerically equal to 6.7V, where V is the speed at any instant time in m/sec. If the boat starts from rest, determine its speed at the end of 10 seconds.arrow_forward
- An elevator starts from rest and moves upward, accelerating at a rate of 1.2 m/s², until it reaches a speed of 6.8 m/s, which it maintains. 2.0 seconds after the elevator starts moving, a man 36 m above the initial position of the elevator throws a ball upward with an initial velocity of 27.5 m/s. Determine the time it will take the elevator to hit the ball, in seconds.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_forwardAn advanced spatial disorientation trainer allows the cab to rotate around multiple axes as well as to extend inwards and outwards. It can be used to simulate driving, fixed-wing aircraft flying, and helicopter maneuvering. In one training scenario, the trainer rotates and translates in the horizontal plane where the location of the pilot is defined by the relationships where r,0, and t are expressed in feet, radians, and seconds, respectively. Knowing that the pilot has a weight of 175 lbs, (a) determine the magnitude of the resulting force acting on the pilot at t= 5 s, (b) plot the magnitudes of the radial and transverse components of the force exerted on the pilot from 0 to 10 seconds.arrow_forward
- The 2013 World Record for the 100 m sprint is 9.75 seconds and belongs to an American runner named Tyson Gay. Assuming constant acceleration, determine the speed of Mr. Gay at distances of 10 m, 20 m, 30 m, …, 80 m, 90 m, and 100 m.arrow_forwardIt is shown in mechanics of materials that the stiffness of an elastic cable is k=AE It is shown in mechanics of materials that the stiffness of an elastic cable is L, where A is the cross-sectional area of the cable, E is the modulus of elasticity, and L is the length of the cable. A winch is lowering a 4000-lb piece of machinery using a constant speed of 3 ft/s when the winch suddenly stops. Knowing that the steel cable has a diameter of 0.4 in., E = 29 × 106 lb/in2, and when the winch stops L = 30 ft, determine the maximum downward displacement of the piece of machinery from the point it was when the winch stopped.arrow_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_forward
- A model rocket is launched from point A with an initial velocity, V₀, of 85 m/s. If the rocket’s descent parachute does not deploy and the rocket lands 100 m from A, 1. Determine the angle α that V₀ forms with the vertical. a. 3.90˚ b. 2.35˚ c. 2.25˚ d. 5.25˚ 2. Determine the maximum height, h, reached by the rocket. * 1 point a. 815 m b. 366 m c. 129 m d. 194 m 3. Determine the duration of the flight. a. 13.4 sec b. 17.3 sec c. 11.6 sec d. 10.4 secarrow_forwardA 4-lblb ball BB is traveling around in a circle of radius r1r1 = 3 ftft with a speed (vB)1(vB)1 = 6 ft/sft/s. The attached cord is pulled down through the hole with a constant speed vrvr = 2 ft/sft/s.(Figure 1) (A) Determine how much time is required for the ball to reach a speed of 12 ft/s. Neglect friction and the size of the ball. Express your answer to three significant figures and include the appropriate units. (B) How far r2 is the ball from the hole when this occurs? Neglect friction and the size of the ball. Express your answer to three significant figures and include the appropriate unitsarrow_forwardA police car is traveling north on a straight road at a constant20.0 m>s. An SUV traveling north at 30.0 m>s passes the police car. Thedriver of the SUV suspects he may be exceeding the speed limit, sojust as he passes the police car he lets the SUV slow down at a constant1.80 m>s2. How much time elapses from when the SUV passes the police car to when the police car passes the SUV?arrow_forward
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