You are standing on the ground at the origin of a coordinate system. An airplane

Question

You are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the x axis and at a constant height of 9.00 Times 10^3 m. At t = 0, the airplane is directly above you so that the vector leading from you to it is P_0 rightarrow = 9.00 Times 10^3 j m. At t = 30.0 s the position vector leading from you to the airplane is P rightarrow_30 = (7.32 Times 10^3 i + 9.00 Times 10^3 j) m as suggested in the figure below. Determine the magnitude and orientation of the airplane's position vector at t = 75.0 s. magnitude m direction degree above the horizontal

Explanation / Answer

here,

P(30) = (7.32 i + 9 j )* 10^3 m

let the horizontal velocity of plane be vx

vx * 30 = 7320

vx = 244 m/s

at t = 75 s

P(75) = vx * 75 i + 9000 j m

P(75) = 18300 i + 9000 j m

magnitude , |P| = sqrt(18300^2 + 9000^2) = 2 * 10^4 m

theta = arctan(9000/18300) = 26.2 degree above the horizontal

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