Answer to Question #225821 in Physics for Gel

Question

A racing boat set out from the dock and speeds away at different velocities to reach the set checkpoints. The table below shows the checkpoints location and time taken by the boat to reach them:

Location: Time Taken by the boat to reach checkpoint:

A= 50m, west from the dock. 2 minutes

B= 100m, 70 degree north of east. 5 minutes

C= 40m, 35 degree south of east from 1min and 30s

checkpoint B.

Calculate the magnitude and direction of the resultant vector. Use analytical method for your solution and include graph with scaling for dimensional analysis.

Answer 1

We have:

A= 50m, west from the dock. 2 minutes

B= 100m, 70 degree north of east. 5 minutes

C= 40m, 35 degree south of east from 1min and 30s

checkpoint B.

So, assume that direction N is +j, E is +i, then we have

$$\vec D=\vec D_A+\vec D_B+\vec D_C,\\ \vec D=[50(-i)]+[100(j\sin70­°+i\cos70°)]+\\+[40(i\cos35°-j\sin35°)]=\\ =17i+71j,\\\space\\ |\vec D|=\sqrt{17^2+71^2}=73\text{ m}.\\\space\\ ­\theta=\arctan\frac{71}{17}=77°\text{ N of E}.$$