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Based on observations, the speed of a jogger can be approximated by the relation
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- At a certain point in the reentry of the space shuttle into the earth's atmosphere, the total acceleration of the shuttle may be represented by two components. One component is the gravitational acceleration g = 9.67 m/s² at this altitude. The second component equals 10.66 m/s² due to atmospheric resistance and is directed opposite to the velocity. The shuttle is at an altitude of 49.6 km and has reduced its orbital velocity of 28300 km/h to 16160 km/h in the direction = 1.23°. For this instant, calculate the radius of curvature of the path and the rate i at which the speed is changing. Answers: p= i = i i km m/s²arrow_forwardAt a certain point in the reentry of the space shuttle into the earth's atmosphere, the total acceleration of the shuttle may be represented by two components. One component is the gravitational acceleration g = 9.60 m/s2 at this altitude. The second component equals 10.28 m/s² due to atmospheric resistance and is directed opposite to the velocity. The shuttle is at an altitude of 46.1 km and has reduced its orbital velocity of 28300 km/h to 16920 km/h in the direction 0 = 1.78°. For this instant, calculate the radius of curvature of the path and the rate i at which the speed is changing. Answers: p= v = i i km m/s²arrow_forwardAt a certain point in the reentry of the space shuttle into the earth's atmosphere, the total acceleration of the shuttle may be represented by two components. One component is the gravitational acceleration g = 9.56 m/s2 at this altitude. The second component equals 11.25 m/s² due to atmospheric resistance and is directed opposite to the velocity. The shuttle is at an altitude of 47.9 km and has reduced its orbital velocity of 28300 km/h to 14750 km/h in the direction = 1.88°. For this instant, calculate the radius of curvature of the path and the rate i at which the speed is changing. Answers: p= i = i FU km m/s²arrow_forward
- applied mechanics 2arrow_forwardIn the development of racing cars, an important parameter is handling. And a measure of handling is turnability which is quantified by the so-called lateral acceleration measured in g's (g = acceleration due to gravity = 9.81 m/s). A prototype racing car is said to be capable of lateral accelerations of up to 1.6 g's. Determine its top speed on curved roads having a radius of curvature of: (a) 100 m, (b) 50 m, (c) 25 m, and (d) 10 m.arrow_forwardI need help with this question please. thank youarrow_forward
- Jack run on a marathon with a speed that can be approximated by the relation v= 6.5(1.2 - 0.05x) ^ 0.3, where v and x are expressed in mi/h and miles respectively. Knowing that x= 0 at t = 0, determine (a.) the distance Jack has run when t =1h, (b) Jack's acceleration in ft/s^2 at t=0, (c.) the time required for him to run 6 mi. helppparrow_forwardmoments = 0) in order to determine a force or moment requires a complete free body diagram. Absence of a free body diagram may result in a grade of 'O' for the problem. %3D 1. The acceleration of a particle is directly proportional to time, t, i.e., a = at where a is a constant. At t = 0 s, the position of the particle is -150 mm. Knowing that v = 200 mm/s and x = 75 mm whent = 3 s, determine the position and velocity when t = 5 s.arrow_forwardThe acceleration of a particle moving along the x-axis is given by the relation a = kt m/s?., where k is a constant, and i is in seconds. Supposed that v = -10 m/s, x = x, when / = 0 and x = 0, v = 0 when t = 6 s, determine (a) the value of the constants k and x,, (b) the position as a function of t. %3Darrow_forward
- Dr. Wang was doing donuts (i.e. driving in a circle) in his car over the weekend and used his iPhone to measure the acceleration he experienced (this is a true story). The plot below shows the lateral acceleration recorded by his iPhone. Knowing that he was maintaining a constant speed and that the radius of his donuts was 10 meters, determine how fast he was driving and approximately how many donuts (laps) did he completed in the 6 seconds shown?arrow_forward3) Two particles, A & B, move along parallel rectilinear paths. At t=0 the particles are directly opposite one another. Particle A moves according to SA = 12t² - 4t³ inches and particle B moves with a constant speed of 12 inches/ second. (a) Determine the relative position of A with respect to B at t = 1 second. (b) Determine the relative velocity of A with respect to B at t = 1 second. ANS. SA/B = -4 inches VA/B = 0 inches/secarrow_forward1) Some civil engineers are designing an Autobahn connecting Reno and Vegas to reduce the drive time. There are several hilly stretches between the two cities. They would like to keep the magnitude of acceleration on the drivers to be less than one g. They run a test where the speed of a biker decreased uniformly with time from 150 km/h at A to 100 km/h at B over 10 seconds. The radius of curvature for dip A is 200 m. If the magnitude of the total acceleration of the center of the mass of the bike is the same at B as at A, compute the radius of curvature rs of the hill in the road at B. The center of the mass of the car is 0.5 m from the road. [Ans. To Check: re-88.5m] TA = 200 m A VA= 150 km/h H = 0.5 m B VB = 100 km/h TB = ? marrow_forward
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