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# Vector Kinematics

If you're in an Airbus 320 cruising at 600 mph, with a 150 mph crosswind, chances are you won't have a strong WiFi signal. Learn vector kinematics now, before you fly.

# Total displacement from velocity vectors

A rocket initially at $$(0,0)$$ moves with a constant velocity of $$(7\text{ m/s},6\text{ m/s})$$ through vacuum. After moving for $$54\text{ s},$$ an asteroid hits the rocket and a change of $$(1\text{ m/s},0)$$ is made to the rocket's velocity. What is the position vector of the rocket at $$t=60\text{ s}?$$

A man initially at $$(0,0)$$ on the coordinate plane walks with a velocity of $$(3\text{ m/s},-\sqrt{5}\text{ m/s})$$ for $$2$$ seconds. Then he walks with a velocity of $$(-1\text{ m/s}, 1\text{ m/s})$$ for $$3$$ seconds. Find the magnitude of his total displacement.

A kayaker paddles due north at 2 m/s. The river the kayaker is paddling in flows towards the east at 1 m/s. After 5 seconds of paddling, how far is the kayaker from where she started in meters?

You wish to swim across a small river to your friend on the other side. The river is 30 meters wide and you begin to swim straight across it at a speed of 1 m/s. The current in the river is 0.5 m/s and so the river carries you downriver as you swim. How far downriver in meters are you when you get to the other side?

A train is moving at a constant speed of $$80\text{ km/h}.$$ The train first moves in the $$+x$$ direction for an hour. Then it turns $$60^{\circ}$$ upward and moves for two hours. Find the magnitude of the train's total displacement.

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