Experimental data indicate that in a region downstream of a given louvered supply vent the velocity of the emitted air is defined by
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- The displacement of a machine is expressed as x(t) = A sin(6t + 0), where x is in meters and t is in seconds. If the displacement and the velocity of the machine at t = 0 are known to be 0.05 m and 0.005 m/s, maximum displacement of the system.arrow_forwardA liquid of specific gravity of 1.75 flows in a 6 cm horizontal pipe. The total energy at certain point in the flow is 80 J/N (joules/newton). The elevation of the pipe above the fixed datum is 2.6 m. If the pressure is 75 kPa. Determine the velocity of flow in m/s. a.37.85 b.32.45 c.42.25 d.23.86arrow_forwardDetermine the magnitude of the velocity of boat A with respect to boat B. Two boats leave the shore at the same time and travel in the directions shown in (Figure 1). vA = 12 m/s and vg = 19 m/s Express your answer to three significant figures and include the appropriate units. HẢ ? VA/B = Value Units Submit Request Answer Part B Determine the direction angle of the velocity of boat A with respect to boat B, measured counterclockwise from the positive a axis. Express your answer using three significant figures. ΠVα ΑΣφ It vec ? Figure Submit Request Answer Part C How long after leaving the shore will the boats be 760 m apart? Express your answer using three significant figures. \30 Πνα ΑΣφ It vec ? 45° t =arrow_forward
- The displacement of a machine is expressed as x(t) = A sin(6t + ®), where x is in meters and t is in seconds. If the displacement and the velocity of the machine at t = 0 are known to be 0.05 m and 0.005 m/s, determine the time it takes for the system to complete one cycle.arrow_forwardQ8. The acceleration of a particle moving along a straight line is a = (C.t-1) m/s2, where Cis a constant and t is the time in s. If the constant Cis 3.6, and the initial velocity vo = 2.1 m/s at time t = 0, determine the particle's velocity when time t = 2 s. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point, and proper Sl unit. Your Answer: Answer unitsarrow_forwardThe position of a particle is given by s = 0.23t³ -0.77t² -2.50t + 5.65, where s is in feet and the time t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 12 seconds of motion. After you have the plots, answer the questions as a check on your work. -+s, ft -1 0 1 2 3 Questions: When t = 1.7 sec, V= ft/sec, ft/sec² When t = 9.8 sec, v = ft/sec, ft/sec² The positive time at which the particle changes direction is i i a = i a = sec.arrow_forward
- The position of a particle is given by s= 0.39³ -0.69t2-2.04t+4.42, where s is in feet and the time t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 6 seconds of motion. After you have the plots, answer the questions as a check on your work. Questions: 0 Whent 0.8 sec, v= When t 5.2 sec, v= 2 3 -+s, ft ft/sec. a ft/sec, a The positive time at which the particle changes direction is i sec. ft/sec2 ft/sec²arrow_forwardIf a ball is thrown into the air with a velocity of 52 ft/s, its height in feet t seconds later is given by y = 52t – 16t2. (a) Find the average velocity for the time period beginning when t = 2 and lasting for each of the following. (i) 0.5 seconds 70 X ft/s (ii) 0.1 seconds 69.5 X ft/s (iii) 0.05 seconds 68.5 ft/s (iv) 0.01 seconds 70 X ft/s (b) Estimate the instantaneous velocity when t = 2. 70 X ft/sarrow_forwardTo use the principle of linear impulse and momentum to relate a force on an object to the resulting velocity of the object at different times. The equation of motion for a particle of mass m can be written as ∑F=ma=mdvdt By rearranging the terms and integrating, this equation becomes the principle of linear impulse and momentum: ∑∫t2t1Fdt=m∫v2v1dv=mv2−mv1 For problem-solving purposes, this principle is often rewritten as mv1+∑∫t2t1Fdt=mv2 The integral ∫Fdt is called the linear impulse, I, and the vector mv is called the particle's linear momentum. A jetliner of mass 8.60×104 kg is in level flight when it encounters a downdraft (a downward wind) that lasts for 1.40 s . The vertical component of the jetliner's velocity is 74.0 m/s after the downdraft subsides. What is the downdraft's average force, F, on the jetliner?arrow_forward
- A boat is towed at the rate of 12mi/hr. At t = 0, the towing line is cast off and a man in the boat begins to row in the direction of motion exerting force of 20 lb. The combined weight of the man and the boat is 480lb. The water resists the motion with a force equal to 1.7v lb, where v is the velocity of the boat in feet per second. Derive a DE leading the velocity of the boat.arrow_forwardTo use the principle of linear impulse and momentum to relate a force on an object to the resulting velocity of the object at different times. The equation of motion for a particle of mass m can be written as ∑F=ma=mdvdt By rearranging the terms and integrating, this equation becomes the principle of linear impulse and momentum: ∑∫t2t1Fdt=m∫v2v1dv=mv2−mv1 For problem-solving purposes, this principle is often rewritten as mv1+∑∫t2t1Fdt=mv2 The integral ∫Fdt is called the linear impulse, I, and the vector mv is called the particle's linear momentum. A stop block, s, prevents a crate from sliding down a θ = 20.0 ∘ incline. (Figure 1) A tensile force F=(F0t) N acts on the crate parallel to the incline, where F0 = 265 N/s . If the coefficients of static and kinetic friction between the crate and the incline are μs = 0.290 and μk = 0.195, respectively, and the crate has a mass of 57.4 kg , how long will it take until the crate reaches a velocity of 3.01 m/s as it moves up the incline?arrow_forwardAn object of mass 2 kg is subjected to a varying force, and it moves along a straight line with time dependent acceleration. The acceleration of the object is given by à(t) = [(2t3 + +2)1 + (1.5t - 0.5)}] m/s, where t is time in seconds. Initially, the object is at rest (initial velocity = 0, t = 0). Determine the magnitude of the velocity of the object at t = 4 seconds.arrow_forward
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