Classical Mechanics

Vector Kinematics

Problem solving with vector kinematics - beginners

         

A lady goes on a hike for 90 minutes. 90 \text{ minutes}. Her average speed is 8 km/h, 8 \text{ km/h}, and she hikes in a direction that makes a 60 60^\circ angle with the eastward and a 3030^\circ angle with the northward. Express her displacement using two direction components.

Assume that 3 \sqrt{3} is approximately 1.7.1.7.

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

Immediately after a ship sets out to sail 150 km150 \text{ km} north, an unexpected storm blows the ship to a point 140 km 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 km/h 40.0 \text{ km/h} due west for 60 minutes, 60 \text{ minutes}, then due north at 20.0 km/h 20.0 \text{ km/h} for 90 minutes. 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 m/s2g = 10 \text{ m/s}^2

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