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The acceleration due to gravity of a particle falling toward the earth is
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Vector Mechanics for Engineers: Dynamics
- The resistance force due to water acting on a boat is proportional to its instantaneous speed, and is such that at 30 feet per second it is 90 pounds. If the boat and its only passenger together weigh 448 pounds and the motor can exert a constant force of 540 pounds in the direction of motion, determine the speed v (t) of the boat, in ft / s, depending on time t, in seconds , assuming that the boat starts from rest. Consider the acceleration of gravity as g = 32 ft / s²arrow_forwardTwo airplanes are performing at an air show. Plane B enters the circular path (r =105 meters) at point O with a velocity of (vB)o = 48 m, which is increasing at a rate of 0.007s2 m. where "s" is the arc length measured from point O in meters. Plane A is travelling along a straight inclined path (0= 38°) and has a constant velocity of va = 132 m. Determine the magnitude of the velocity vector of plane B (in m) when it has travelled 30° around the circular path. A 30 y В -arrow_forwardplease help my head really hurts just by looking at this onearrow_forward
- The basketball passed through the hoop even though it barely cleared the hands of the player B who attempted to block it. Suppose that s = 5 ft. Neglect the size of the ball. 10 ft 25 n Part A Determine the magnitude v of its initial velocity. Express your answer to three significant figures and include the appropriate units. VA= Part B Determine the height h of the ball when it passes over player B. Express your answer to three significant figures and include the appropriate units. h =arrow_forward1) A subway train starts from rest at a station and accelerates at a rate of 1.6 m/s² for 14 seconds. It runs at constant speed for 70 seconds and slows down at a rate of 3.5 m/s² until it stops at the next station. Find the total distance covered by the subway train.arrow_forwardThe force exerted by the motor M on the cable is shown in the graph. (Figure 1) Part A: Determine the velocity of the 155-lb crate A when t=2.5s. Express your answer in feet per second to three significant figures. F (lb) 250 lb- M t (s) 2.5 Aarrow_forward
- A small toy car moves around a circular track with a 1 m radius. It starts at rest, and increases its speed at a constant rate of v = 0.8 m/s². The car will come off of the track when a ≥ 5 m/s². How many revolutions of the track will the car complete before it comes off the track? Enter a decimal number for partial revolutions. revolutionsarrow_forwardUBC Engin A trebuchet uses a falling counterweight to launch a projectile. It can be thought of as a machine that converts the gravitational potential energy of the counterweight into kinetic and gravitational potential energy of the projectile. The counterweight has a mass of 100kg and drops 3m. The projectile has a mass of 3kg, and starts on the ground. When it leaves the sling, it has a height of 4m speed of 30. m If the average power used in lifting the counterweight is 48W, find the time it takes to lift it from the ground to its full height. tlifting If the projectile goes from rest to its maximum speed in 1.5s. find the average power used in launching the projectile in this time period. Pprojectile Find the efficiency of the trebuchet when it launches. Efficiency % Warrow_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
- A rocket sled is a test platform that slides along a set of rails, propelled by rockets. During a trail rocket sled starts from rest and experiences an acceleration of a = 3t2 m/s2 until its velocity is 1000 m/s. It then hits brakes and accelerate with a = -0.001V2 m/s2 until its velocity decreases to 500 m/s. Calculate the total distance travelled by sled.arrow_forwardA 100-kg box is towed to move horizontally from rest by a constant force P=200 N. The kinetic friction is μk =0.1. The angle of the force P is θ=30° with respect to the horizontal direction. The acceleration due to gravity is g=9.81 m/s2. (7) Calculate the the velocity at 2 seconds v= ___(m/s ) (two decimal places).arrow_forwardThe resultant force on a particle is given as EF = 2t³i + (3t² − 1)j + (5t - t²)k Newton where t is in seconds. If the mass of the particle is m = 1.5 kg, what is the magnitude of the acceleration of the particle at t = 1 s? 3.27 m/s² 4.90 m/s² O 7.35 m/s² O 1.5 m/s²arrow_forward
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