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A small boat is headed for a harbor 35 km directly northwest of itscurrent position when it is suddenly engulfed in heavy fog. Thecaptain maintains a compass bearing of northwest and a speed of10.1 km/h relative to the water. The fog lifts 3.0 h later and thecaptain notes that he is now exactly 3.6 km south of theharbor.

(a) What was the average speed of the current during those 3.0h?
km/h

(b) In what direction should the boat have been heading to reachits destination along a straight course?
°west of north

(c) What would its travel time have been if it had followed astraight course?
h

Determine the energy change for the following reaction:

Methane + oxygen produces carbon dioxide + water.

A boat whose speed is 8km/h sets course on bearing of 60 degrees .if the tide is running at  a speed of 3km/h from the bearing of 330 degrees .find 

(I)the actual speed of the boat 

1. (ii)the direction of the boat

 The drawing shows a square, each side of which has a length of . On two corners of the square are fixed different positive charge . Find the electric potential energy of a third charge placed at corner A and then at corner B.

A square sheet has a uniform surface charge densityσσ. Letting the electric potential ϕϕ be zero at infinite distance from the square, denote by ϕ0   the potential at the center of the square and by ϕ1   the potential at a corner. Determine the ratio    .

The answer can be found with very little calculation by combining a dimensional argument with superposition. (Think about the potential at the center of a square with the same charge density and with twice the edge length.)

A reaction that generates heat energy is the combustion of methane with oxygen gas to produce carbon dioxide and water. If 3.2 g of methane reacts with 16.5 g of oxygen to produce 9.2 g of water, how many grams of carbon dioxide are also formed?

Determine the energy change for the following reaction 

Methane + oxygen produces carbon dioxide + water