A small boat is crossing a lake on a windy day. During some interval of time, the boat undergoes the given displacement Δ → r. Δ → r = (3.29 m) ^ ı + (2.67 m) ^ ȷ During the same interval of time, the wind exerts the given constant force → F on the boat. → F = (281 N) ^ ı - (135 N) ^ ȷ What is the total work done on the boat by the wind over this period of time?

564.04Nm

Explanation:

Work is said to be dome when an applied force on an object cause the object to move through a distance. Mathematically;

Work done = Force * Distance in the direction of the force

Given the displacement

r = (3.29 m) ^ ı + (2.67 m) ^ ȷ

Force F = (281 N) ^ ı - (135 N) ^ ȷ

Vectorially, i. i = j. j = 1 and i. j = 0 (dot product of different components gives 0)

Work done F = { (281 N) ^ ı - (135N) ^ȷ} * { (3.29 m) ^ı + (2.67 m) ^ȷ}

Multiplying both vectors will give;

= 281i (3.29i) + 281i (2.67j) - 135j (3.29i) - 135j (2.67j)

Since i. j = 0 and i. I = j. j = 1, the answer becomes;

= 924.49 (i. i) - 360.45 (j. j)

= 924.49-360.45

= 564.04Nm

The total work done is 564.04Nm