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.