Q:

A hiker walks 4 km north and then 5 km northeast. Draw displacement vectors representing the hiker's trip and draw a vector that represents the hiker's net displacement from the starting point.

Accepted Solution

A:
Answer:[tex]u+v =8.323717394km[/tex] Ф=[tex]64.86489406[/tex]°Step-by-step explanation:[tex]u=4km[/tex][tex]v=5km[/tex]For easy calculations let's decompose the vector in its rectangular components:[tex]u_x=u*cos(\alpha )=4000*cos(90)=4000*0=0[/tex][tex]u_y=u*sin(\alpha )=5000*sin(90)=4000*1=4000[/tex][tex]v_x=v*cos(\beta )=5000*cos(45)=3535.533906[/tex][tex]v_y=v*sin(\beta )=5000*sin(45)=3535.533906[/tex]Now lets calculate the resultant vector:[tex]u+v=R[/tex][tex]R=R_x+R_y[/tex][tex]R_x=u_x+v_x=0+3535.533906=3535.533906[/tex][tex]R_x=u_y+v_y=4000+3535.533906=7535.533906[/tex]Finally let´s calculate the magnitude and direction of R:║[tex]R[/tex]║=[tex]\sqrt{(R_x)^{2}+(R_y)^{2}  }=\sqrt{(3535.533906)^{2}+(7535.533906)^{2}  }  =8.323717394km[/tex]Ф=[tex]arctan(\frac{R_y}{R_x})=arctan(\frac{7535.533906}{3535.533906})=64.86489406[/tex]°