A particle travels with speed $$50$$ $$m/s$$ from the point (3$$ m, $$-7$$ $$m) in a direction $$7i^$$−$$24j^$$. Find its position vector after $$3$$ seconds.

Question

A particle travels with speed $$50$$ $$m/s$$ from the point (3$$ m, $$-7$$ $$m) in a direction $$7i^$$−$$24j^$$. Find its position vector after $$3$$ seconds.

Infinity Learn · Accepted Answer

Given speed $$v=50m/s$$ in the direction a→$$=7i^$$−$$24j^v$$→$$=va^$$;$$a^$$ is the unit vector in the direction $$7i^$$−$$24j^a^=(7i^$$−$$24j^)(24)2+(7)2=(7i^$$−$$24j^)25v$$→$$=va^=50$$⋅$$(7i^$$−$$24j^)25=2(7i^$$−$$24j^)m/s$$ Initially the particle is at r→$$0=(3i^$$−$$7j^)m$$ Position of the particle after $$3sec$$,r→$$=r$$→$$0+v$$→t⇒ r→$$=(3i^$$−$$7j^)+3$$×$$2(7i^$$−$$24j^)=(45i^$$−$$151j^)m$$

A particle travels with speed 50 m/s from the point (3 m, -7 m) in a direction $7 \hat{i} - 24 \hat{j}$ . Find its position vector after 3 seconds.

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A particle travels with speed 50 m/s from the point (3 m, -7 m) in a direction 7i^−24j^. Find its position vector after 3 seconds.

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A particle travels with speed 50 m/s from the point (3 m, -7 m) in a direction $7 \hat{i} - 24 \hat{j}$ . Find its position vector after 3 seconds.