Question

Suppose Madison is traveling due west for 0.5 miles and then due south for 1.2 miles.

a. Draw a picture of this scenario with her starting point labeled A, ending point B, and include the vector AB????⃗.
b. State the value of AB????⃗.
c. What is the magnitude and direction of AB

Answer 1

b) 1.3 units

b) 22.61° East of North

Explanation:

`|\vec{AB}|=√(0.5^2+1.2^2)\\\Rightarrow |\vec{AB}|=√(0.25+1.44)\\\Rightarrow |\vec{AB}|=√(1.69)\\\Rightarrow |\vec{AB}|=1.3`

`|\vec{AB}|=1.3\ units`

Magnitude of vector AB is 1.3 units

`tan\theta=(0.5)/(1.2)\\\Rightarrow \theta=tan^(-1)(0.5)/(1.2)\\\Rightarrow \theta=22.61^(\circ)`

The direction of vector AB is 22.61° East of North