, (13%) Problem 9: Two cars are heading towards one another. Car A is moving wit

Question

, (13%) Problem 9: Two cars are heading towards one another. Car A is moving with an acceleration of ad-7 msCar B is moving with an acceleration of aB =-13 m s'·The cars are initially at rest and separated by a distance d= 4950 m on the x-axis 25% Part (a) At what time, in seconds, do the cars meet? Grade Summary Deductions Potential 0% 100% 7 8 9 sin0 cotan0asin acos0 atan0 acotan sinhO cosh0 tanh cotanh0 cosO tan Submissions Attempts r (2% per attempt) detailed view emaining: 6 END Degrees Radians NO Submit Hint I give up! Hints: 2% deduction per hint. Hints remaining: 3 Feedback: 0% deduction per feedback. 25% Part (b) What is the displacement, in meters, of Car A? 25% Part (c) What is the displacement, in meters, of Car B? 25% Part (d) Now assume that both cars start with an initial velocity. Car A's initial velocity is V0A 44 ms and Car B's initial velocity s vB = -29 m/s. At what time, t in seconds, do they meet?

Explanation / Answer

Given

two cars A and B moving with accelerations

aA = 7 m/s2 and aB = -13 m/s2 from rest, and separated by a distance of d = 4950 m/s

from equations of motions

s = ut+0.5*a*t^2

total displacement is s = 0.5*aA*t^2 +0.5*aB*t^2

now the time taken is

4950 = 0.5*t^2(aA+aB)

4950 = 0.5*t^2(7+13)

solving for t, t = 22.25 s

part (a)

the cars can meet at t = 22.25 s, after their start

Part (b)

the displacement the carA can make in 22.25 s is

s = ut+0.5*at^2

s = 0*t+ 0.5*7*22.25^2 m = 1732.72 m

Part (c)

the displacement the carB can make in 22.25 s is

s = ut+0.5*at^2

s = 0*t+ 0.5*13*22.25^2 m = 3217.91 m

part (d)

now initial velocities of the cars are v0A = 44 m/s ,v0B= -29 m/s

4950 /(44+29) = 67.80 s

so they can meet at t2= 67.80 s

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