A student observes an airplane fly overhead with a constant velocity parallel to

Question

A student observes an airplane fly overhead with a constant velocity parallel to the x-axis at a height of 7.60 x 10^3 m. At time t = 0 the airplane is directly above the student, the vector P0 = 7.60 x 10^3j m describes the position on the airplane with respect to the student. At time t = 30.0 s, the position vector has changed to P_30 = (8.04 x 10^3z + 7.60 x 10^3j m as shown in the figure below. Ignore drag. Determine the magnitude and orientation of the airplane's position vector at t = 45.0 Write down a time-dependent vector Pt that describes the position of the airplane with respect to the student at any time after t = 0.

Explanation / Answer

at t=o

xo =0

y0 =7.6*10^3 j

at t =30 s

P30 = (8.04*10^3 i)+(7.6*10^3)j

x30 = 8.04*10^3

From kinematic equaiton along x axis

x -xo = uxt+(1/2)axt^2

8.04*10^3 - 0 = 0+(0.5*a*30*30)

ax = 17.87 m/s^2

(a) at t=45 s

x =xo+(1/2)axt^2 = (0.5*17.87*45*45)

x= 18.1*10^3

P40 = (18.1*10^3)i+(7.6*10^3)j

P40 =10^3((18.1)^2+(7.6)^2)^1/2

Magnitude P40 = 19.63*10^3 m

direction tan(theta) = 7.6/18.1

theta = 22.8 degrees with positive x axis

(b) Pt = (8.935t^2)i+(7.6*10^3)j

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