(a) The current in a river flows at 1.35 ms-1 relative to an observer on the shore. A swimmer with a velocity of 3.12 ms-1 relative to the water swims directly upstream. What is the velocity of the swimmer relative to an observer on the shore?

i used v=v water + v swimmer
-1.35 + 3.12 = 1.77 is this correct ?

Vs = 3.12 - 1.35 = 1.77 m/s.

Yes, your calculation is correct. To find the velocity of the swimmer relative to an observer on the shore, you can use the formula:

v = v_water + v_swimmer

Where:
v = velocity of the swimmer relative to the observer on the shore
v_water = velocity of the river current relative to the observer on the shore (given as -1.35 m/s, indicating it flows in the opposite direction to the swimmer)
v_swimmer = velocity of the swimmer relative to the water (given as 3.12 m/s)

Substituting the given values into the equation:

v = -1.35 m/s + 3.12 m/s
v = 1.77 m/s

So, the velocity of the swimmer relative to an observer on the shore is 1.77 m/s.