A bird moves from point (1, -2) to (4, 2). If the speed of the bird is 10 m/sec, then the velocity vector of the bird is
Question
A bird moves from point (1, -2) to (4, 2). If the speed of the bird is 10 m/sec, then the velocity vector of the bird is
Solution
To find the velocity vector of the bird, we first need to find the displacement vector. The displacement vector is the difference between the final and initial positions of the bird.
The initial position of the bird is at point (1, -2) and the final position is at point (4, 2).
So, the displacement vector Δr = r(final) - r(initial) = (4, 2) - (1, -2) = (4-1, 2-(-2)) = (3, 4).
The magnitude of the displacement vector |Δr| = sqrt((3)^2 + (4)^2) = 5 units.
The direction of the displacement vector is given by the angle θ = tan^-1(4/3) = 53.13 degrees.
The velocity of the bird is given by the vector v = Δr/t, where t is the time taken.
Since the speed of the bird is given as 10 m/s, and the magnitude of the displacement is 5 units, the time taken t = |Δr|/speed = 5/10 = 0.5 seconds.
So, the velocity vector of the bird is v = Δr/t = (3, 4)/0.5 = (6, 8) m/s.
This means the bird is moving at a speed of 10 m/s in the direction described by the vector (6, 8).
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