Vector Kinematics
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.
Consider \(g = 10 \text{ m/s}^2\)