The velocity vector of a ball is v(t)=-3x+4y at any time. Its initial position i

Question

The velocity vector of a ball is v(t)=-3x+4y at any time. Its initial position is r=12x-4y. The components of the velocity vector are in m/s and the components of the position vector are in meters. The symbols x and y are the unit vectors in x and y directions respectively. Find the magnitude of the velocity vector and the angle it makes with the positive x-axis. Find the component form (using the unit vectors x and y) the displacement vector 2 seconds later. Find the final position vector in component form at the end of 2 seconds. Find the average acceleration vector.

Explanation / Answer

a) The magnitude of velocity vector = v= sqrt [(-3)^2 + (4)^2]

v= 5m/s

theta = atan(-4/3) = -88.67 deg

Projection = 180-theta = 180+88.67 =268.67 deg

b) Displacement in component form after 2 seconds, D = 2 y

c) position vector after 2 seconds = -3/2 x +2 y

d)Average acceleration = a= 5/2 +5/2 = 5 m/s^2

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