This print-out should have 6 questions. Multiple-choice questions may continue o

Question

This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. A car is parked near a cliff overlooking the ocean on an incline that makes an angle of 21.7 degree with the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes arc defective. The car rolls from rest down the incline and has a velocity 5 m/s when it reaches the edge of the cliff is 19.4 m above the ocean. What is the y component of velocity after 1 s' Answer in units of m/s. What is the magnitude of the displacement from the origin (z = 0 m. y = 0 m) after 1 s' Answer in units of m. How far is the car from the base of the cliff when the car hits the ocean? The acceleration of gravity is 9.8 m/s^2. Answer in units of m. A particle at rest undergo an acceleration. At time zero, the particle is at x = 9 m, y = 8.5 m, and has velocity upsilon_0 = (9m/s) i + (-7 m/s) j. the acceleration is given by a = (8.5 m/s^2) i + (6.5 m/s^2)j. What is the x component of velocity after 1 s? What is the y component of velocity after 1 s? What is the magnitude of the displacement from the origin (x = 0 m, y = 0) after 1 s?

Explanation / Answer

Part 1 of 2 -

Recall that acceleration [a] is the derivative of velocity with-respect-to (wrt) time, i.e., a = dv/dt.

Then, let ax and ay denote the horizontal (right) and vertical (up) accelerations, respectively, and let vx and vy denote the horizontal and vertical velocities, respectively. Both vx and vy are normal to each other, as are ax and ay.

Now, since the initial acceleration is zero in both directions, the integral of ax wrt time (i.e., the integral of ax dt) gives the velocity vx, and the integral of ay wrt time gives the velocity vy at any time, such as at t = 6.9 s.

So, at t = 6.9,

2.9*6.9= vx = 20.01 m/s,

and

4.3 * 6.9= vy = 29.67 m/s.

(a) The total velocity magnitude (speed) is the square root of the squared orthogonal component velocities, i.e., 35.79m/s.

(b) The horizontal direction is given by the arc tangent of vy/vx

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