This is a sheet of harder questions on vectors.

A river flows at 3.0 km/h. The river is 100.0 m wide and a boat is to arrive on the opposite bank 80.0 m downstream from its starting point. What is the velocity of the boat relative to the water if the time of crossing is 5.0 minutes? [2.4km/h at 31° to the upstream bank]
A river 1.0 km wide flows due north at 8.0 km/h. A motor launch travels at 6.0 km/h relative to the water. A person starts from the west bank and wishes to reach the point directly opposte on the east bank. If the person can walk at 3.0 km/h find the direction in which the motor launch should head so that the person can make the journey in the minimum time.[E33°S]
Relative to a cyclist travelling to the west at 40km/h the wind appears to be coming from the south. On doubling their speed the wind appears to be coming from the south-west. What is the velocity of the wind?[56.6km/h NW]
A cyclist travelling on a straight road at 10 km/h is subject to air resistance proportional to the square of their speed. By what factor must they increase their power output to maintain their speed if a 20 km/h cross wind develops?[5^1/2]
An ocean liner is travelling in a straight line at a speed of 20km/h that takes it 1.0 km from a port. A boat that can travel at 12km/h is to leave the port at the last possible time and move in a straight line to meet the ocean liner. What is the distance travelled by the boat when it reaches the liner? [1.25km]

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