Respuesta :
Given that,
Ice travel = 20.0 m
The direction is 25° W of N
Deflect distance = 30.0 m
The direction is 35° N of W
(I). When ice travel west of north
We need to calculate the displacement
Using formula of displacement of component
[tex]\vec{D}=d\cos\theta+d\sin\theta[/tex]
Put the value into the formula
[tex]\vec{D}=20\cos25(j)+20\sin25(-i)[/tex]
[tex]\vec{D}=18j-8.44i[/tex]
(II). When ice deflect north of west
We need to calculate the displacement
Using formula of displacement of component
[tex]\vec{D'}=d\cos\theta+d\sin\theta[/tex]
Put the value into the formula
[tex]\vec{D'}=30\cos35(-i)+30\sin35(j)[/tex]
[tex]\vec{D'}=-24.3i+17.1j[/tex]
We need to calculate the magnitude puck's total displacement
Using formula for total displacement
[tex]\vec{D''}=\vec{D}+\vec{D'}[/tex]
Put the value into the formula
[tex]\vec{D''}=18j-8.44i-24.3i+17.1j[/tex]
[tex]\vec{D''}=-32.74i+35.1j[/tex]
[tex]|\vec{D''}|=\sqrt{(-32.74)^2+(35.1)^2}[/tex]
[tex]D''=47.9\ m[/tex]
Hence, The magnitude puck's total displacement is 47.9 m.
(ii). Given that,
He shoot the puck 25 m in east.
The displacement is
[tex]\vec{D}=25i+0j[/tex]
A player is positioned 35 m at 40° West of south.
We need to calculate the displacement
Using formula of displacement
[tex]\vec{D'}=d\cos\theta(-i)+d\sin\theta(-j)[/tex]
Put the value into the formula
[tex]\vec{D'}=35\cos40(-i)+35\sin40(-j)[/tex]
[tex]\vec{D'}=-26.81i-22.49j[/tex]
We need to calculate the total displacement
Using formula for total displacement
[tex]\vec{D''}=\vec{D}+\vec{D''}[/tex]
Put the value into the formula
[tex]\vec{D''}=25i+0j-26.81i-22.49j[/tex]
[tex]\vec{D''}=-1.81i-22.49j[/tex]
The magnitude of the total displacement
[tex]|\vec{D''}|=\sqrt{(-1.81)^2+(-22.49)^2}[/tex]
[tex]D''=22.56\ m[/tex]
Hence, The magnitude of the total displacement is 22.56 m
