The velocity of a body at time t = 0 is \(10 \sqrt{2}\) m/s in the north-east direction and it is moving with an acceleration of 2 m/s 2 directed towards the south. The magnitude and direction of the velocity of the body after 5 sec will be
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\vec{v} = \vec{u} + \vec{a} t ∴ ∴ \(v = \sqrt{u^{2} + a^{2} t^{2} + 2 u a t \cos \theta}\)
\(v = \sqrt{200 + 100 + 2 \times 10 \sqrt{2} \times 10 \times \cos 135}\) \(= 10 \mathrm{m/s}\)
\(\tan \alpha = \frac{a t \sin \theta}{u + a t \cos \theta} = \frac{10 \sin 135}{10 \sqrt{2} + 10 \cos 135} = 1\) ∴ ∴ \(\alpha = 45^\circ\)
i.e. resultant velocity is 10 m/s towards East.
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