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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.

# Problem solving with vector kinematics - beginners

A lady goes on a hike for $$90 \text{ minutes}.$$ Her average speed is $$8 \text{ km/h},$$ and she hikes in a direction that makes a $$60^\circ$$ angle with the eastward and a $$30^\circ$$ angle with the northward. Express her displacement using two direction components.

Assume that $$\sqrt{3}$$ is approximately $$1.7.$$

The motion of a creature on a two dimensional plane can be described by the following equations for velocity in $$x \text{ and } y$$ directions: \begin{align} v_x(t)&=6t \\ v_y(t)&=- 2t + 7. \\ \end{align} Find the square of the magnitude of its velocity vector at $$t = 2.$$

Immediately after a ship sets out to sail $$150 \text{ km}$$ north, an unexpected storm blows the ship to a point $$140 \text{ km}$$ east of its starting point. Approximately how far must it now sail to reach its original destination?

A car drives at $$40.0 \text{ km/h}$$ due west for $$60 \text{ minutes},$$ then due north at $$20.0 \text{ km/h}$$ for $$90 \text{ minutes}.$$ Find the magnitude of the car's total displacement.

A car drives straight off the edge of a cliff that is 80 m high. At the scene of the accident you note that the point of impact is 160m from the base of the cliff. How fast was the car traveling in m/s when it went over the cliff?

Consider $$g = 10 \text{ m/s}^2$$

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