A jet plane is flying at a constant altitude. At time t1=0 it has components of

Question

A jet plane is flying at a constant altitude. At time t1=0 it has components of velocity vx= 94 m/s , vy= 115 m/s . At time t2= 28.0 s the components are vx= 174 m/s , vy= 45 m/s .

Part A

For this time interval calculate the average acceleration.

Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures.

PART B -Find the magnitude of the average acceleration.

Express your answer using two significant figures.

Part C

Find the direction of the average acceleration (let the direction be the angle that the vector makes with the +x-axis, measured counterclockwise).

Explanation / Answer

Given velocity vectors
  

   v1 = 94 m/s i +115 m/s j
   v2 = 174 m/s i + 45 m/s j

time intervals t1= 0 s, t2 = 28.0 s, timeperiod is Dt = t2-t1 = 28-0= 28

PART A
   change in velocities is DV = v2- v1 = (174-94)m/si + (45-115)m/s j
               Dv = 80 m/s i - 70 m/s j

now average acceleration is a avg = DV/Dt = 1/28(80 m/s i - 70 m/s j)

               aavg = 2.86 m/s2 i - 2.5 m/s2 j
a avg_x = 2.86 m/s2, a avg_y = -2.5 m/s2
PART B

magnitude of average acceleration is a = sqrt(2.86^2+(-2.5^2)) = 1.39 m/s2

PART C

direction of average acceleration is Tan theta = ay/ax = -2.5/2.86

           theta = arc tan (-2.5/2.86) = -41.16 degrees

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