You are flying a remote controlled airplane over an empty parking lot. You are s

Question

You are flying a remote controlled airplane over an empty parking lot. You are standing in the center of the lot (the origin) and you assume north is the positive y-direction and east is the positive x-direction You can express the plane's motion according to the following equations: v_x = 1.0 m + 2.5 m sin (t + pi/3) V_y = 4.0 m cos (2t) What is the instantaneous velocity of the airplane at t = 2 pi/3 s? Select one: a. v vector = - 4.0 m/s j b. v vector = 3.5 m i - 4.0 m/s j c. v vector = 1.0 m/s i - 2 m/s j v vector = -2.5 m/s i + 6.9 m/s j

Explanation / Answer

Vx = 1 + 2.5*sin (t + pi/3)

at t = 2*pi/3

Vx = 1 + 2.5*sin (2*pi/3 + pi/3)

Vx = 1 + 2.5*sin (3*pi/3)

Vx = 1 + 2.5*sin (pi) = 1 + 2.5*0

Vx = 1 m

Now in y-direction

Vy = 4*cos (2*t)

at t = 2*pi/3

Vy = 4*cos (2*(2*pi/3)) = 4*cos (4*pi/3)

Vy = 4*(-1/2) = -2

V = Vx i + Vy j

So,

V = 1 i - 2 j

Correct option is C.

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