Classical Mechanics

Vector Kinematics

Total displacement from velocity vectors

         

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

A man initially at (0,0)(0,0) on the coordinate plane walks with a velocity of (3 m/s,5 m/s)(3\text{ m/s},-\sqrt{5}\text{ m/s}) for 22 seconds. Then he walks with a velocity of (1 m/s,1 m/s)(-1\text{ m/s}, 1\text{ m/s}) for 33 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 km/h.80\text{ km/h}. The train first moves in the +x+x direction for an hour. Then it turns 6060^{\circ} upward and moves for two hours. Find the magnitude of the train's total displacement.

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