11.167 To study the performance of a racecar, a high-speed camera is positioned at Point A. The camera is mounted on a mechanism which permits it to record the motion of the car as the car travels on straightway BC. Determine (a) the speed of the car in terms of b, 0, and è and (b) the magnitude of the acceleration in terms of b, 0, , and ë. B
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- O Derive theqaahion of Motion in Eorms of height: 2 line for eayylig the fank. f opon 1om そSHOW THE SOLUTION: One morning, Connie walks from her house to go to a store that is 500 ft, S 40o W from her house. She starts walking 120 ft, SW; then continues walking 100 ft, 10o S of E; then sees a friend who is 700 ft, 30o N of E from where she is. What is her friend’s location, (magnitude and direction) relative to her house? (Answer: 667.54 ft, 21.79o N of E) From her friend’s location, how far and in what direction should Connie walk to finally get to the store? (Answer: 1133.08 ft, 33.83o S of W)One morning, Connie walks from her house to go to a store that is 500 ft, S 40o W from her house. She starts walking 120 ft, SW; then continues walking 100 ft, 10o S of E; then sees a friend who is 700 ft, 30o N of E from where she is. What is her friend’s location, (magnitude and direction) relative to her house? (Answer: 667.54 ft, 21.79o N of E)
- One morning, Connie walks from her house to go to a store that is 500 ft, S 40o W from her house. She starts walking 120 ft, SW; then continues walking 100 ft, 10o S of E; then sees a friend who is 700 ft, 30o N of E from where she is. What is her friend’s location, (magnitude and direction) relative to her house? (Ans. 667.54 ft, 21.79o N of E) From her friend’s location, how far and in what direction should Connie walk to finally get to the store? (Ans. 1133.08 ft, 33.83o S of W)A particular bicycle has wheels that are 66 cm in diameter. The radius of the crank armis 18 cm. At its lowest point, the pedal is 16 cm above the ground. A person is pedalingthe bicycle such that the crank arm rotates once every second.Questions:1. Write an equation that models the vertical position of the foot with respect to theground, starting from the lowest point, as the crank arm turns.2. What is the rate of change of the vertical position of the foot when it is at themidline? Explain your answer3. How fast, in kilometres per hour, is the bicycle moving?4. Determine an equation that would model the foot’s position when the cyclist istraveling 5 km/h. Compare this equation to your equation from question 1 andexplain any differences.5. Use calculus to explain why the rotation velocity of a point on the perimeter of awheel is the same as the velocity of the pedal. Use examples to support youranswer.An automobile P is traveling along a circular track of radius R=958.4 m. At position "A" on the track, the automobile has a speed of UA = 10.3 m/s. At this position, the driver of the automobile applies the brakes causing the speed of the automobile to change with distance s traveled along the track according to the following equation: U(S) = VA COS(0.001s) m/s (cos is in radians), where s is given in meters. Determine the magnitude of the acceleration for the driver when the automobile reaches position "B" on the track where "B" is a quarter of the distance around the track from position "A". R B O circular track
- sdasOne morning, Cfonnie walks from her house to go to a store that is 500 ft, S 40o W from her house. She starts walking 120 ft, SW; then continues walking 100 ft, 10o S of E; then sees a friend who is 700 ft, 30o N of E from where she is. What is her friend’s location, (magnitude and direction) relative to her house? (Ans. 667.54 ft, 21.79o N of E)show complete solution and diagramsThe rotation of a 90 cm long OA arm around point O is defined by the equation = 0.15t ^ 2. Here 0 → radyan ve It is measured as. Block B slides on the arm so that its distance from O is = 90 –12t ^ 2. It is expressed here as r → cm ve t → sn. Find the total velocity and total acceleration of the B block when the OA arm rotates 30 °.A car P travels along a straight road with a constant speed v-76 mi/hr. At the instant when the angle 0-46°, determine the values of in ft/sec and 0 in deg/sec. Assume - 106. Answers: 0- 1011 ft/sec deg/sec
- The diagram below represents a swimmer. The swimmer is capable to swim in a still water with a velocity Vị = 1 m's. He aims his body directly across a 100 m wide river whose current has a velocity V;=2 m/s. Use this diagram to answer questions 1 through 3. 1. The time it will take for the swimmer to cross the river is .. (A) 10 sec (B) 20 sec (C) 50 sec (D) 100 sec 2. How far downstream will he land? The correct answer is (A) 100 m (B) 200 m (C) 150 m (D) 180 mc. Derive the piston instantaneous acceleration as a function of the crank angle. . Piston Acceleration Speed dUp dUp d de dt dᎾ - (a sin(0) [1. + = @= cos(0) √R²-sin²( Son ² (1)D) w ²y (m) 2 intervals. The Figure shows the result of a collision of a 10.00 kg ball with an object located at the origin. The position of the objects are shown at 1.3 s -2 06 يه ® © ® Ⓡ • 0 x (m) + 2 What is the mass of the object that was originally located at the origin? What is the change in the kinetic energy as a result of the collision?