A bird moves from a point (1,-2,3) to (4,2,3).If the speed of the bird is 10 m/s, then the velocity vector of the bird is?

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Answer 1 · 2017-07-18T17:09:36

Initial position vector of the bird ${\to r}_{i} = ˆ i - 2 ˆ j + 3 ˆ k$ $vecr_i=hati-2hatj+3hatk$

Final position vector of the bird ${\to r}_{f} = 4 ˆ i + 2 ˆ j + 3 ˆ k$ $vecr_f=4hati+2hatj+3hatk$

So displacement vector

$\to d = {\to r}_{f} - {\to r}_{i}$ $vecd=vecr_f-vecr_i$

$= (4 ˆ i + 2 ˆ j + 3 ˆ k) - (ˆ i - 2 ˆ j + 3 ˆ k)$ $=(4hati+2hatj+3hatk)-(hati-2hatj+3hatk)$

$= 3 ˆ i + 4 ˆ j$ $=3hati+4hatj$

Unit displacement vector

$= \frac{\to d}{∣ ∣ ∣ \to d ∣ ∣ ∣}$ $=(vecd)/abs(vecd)$

$= \frac{3 ˆ i + 4 ˆ j}{∣ ∣ 3 ˆ i + 4 ˆ j ∣ ∣}$ $=(3hati+4hatj)/abs(3hati+4hatj)$

$= \frac{3 ˆ i + 4 ˆ j}{\sqrt{3^{2} + 4^{2}}}$ $=(3hati+4hatj)/sqrt(3^2+4^2)$

$= \frac{3 ˆ i + 4 ˆ j}{5}$ $=(3hati+4hatj)/5$

The direction of velocity is same as that of displacement.

And the magnitude of velocity is $10 m / s$ $10m"/"s$

Hence the velocity vector

$\to v = 10 \times \frac{3 ˆ i + 4 ˆ j}{5}$ $vecv=10xx(3hati+4hatj)/5$ m/s

$\Rightarrow \to v = 6 ˆ i + 8 ˆ j$ $=>vecv=6hati+8hatj$ m/s