91影视

• The magnitude of the winner is in the A direction is,$A=20.8\mathrm{m}$
• The magnitude of the winner is in the B direction is,$B=38.0\mathrm{m}$
• The magnitude of the winner is in the C direction is,$C=18.0\mathrm{m}$

Displacement is defined as straight line distance covered in a certain direction.

A displacement vector is defined as the longest vector whose length equals the smallest distance between the beginning and end positions.

The diagram has been provided below-

The equation of the components of magnitude of the vectors A and B is the x and y direction are given by,

$$\begin{gathered} A_x=A\cos 90掳, \\ {A}_y=A\sin 90掳 \\ {B}_x=B\cos 0掳 \\ {B}_y=B\sin 0掳 \end{gathered}$$

Here,${\mathrm{A}}_x\mathrm{and}{\mathrm{A}}_{\mathrm{Y}}$are the x and y components and the vector A andare the x and y components and the vector B

Substituting the values in the above equation,

$$\begin{gathered} {\mathrm{A}}_{\mathrm{x}}=0, \\ {\mathrm{A}}_{\mathrm{y}}=20.8\mathrm{m}, \\ {\mathrm{B}}_{\mathrm{x}}=38.0\mathrm{m}, \\ {\mathrm{B}}_{\mathrm{y}}=0 \end{gathered}$$

The equation of the components of magnitude of the vectors C is the x and y direction are given by,

$$\begin{gathered} C_x=-C\sin 33掳, \\ {C}_y=-C\cos 33掳, \end{gathered}$$

Here,$C_{\mathrm{x}}\mathrm{and}{\mathrm{C}}_{\mathrm{y}}$are the x and y components and the vector C

Substituting the values in the above equation,

$$\begin{gathered} C_x=-\left(18\mathrm{m}\right)\left(\sin 33.0掳\right) \\ =-9.80\mathrm{m} \\ {\mathrm{C}}_{\mathrm{y}}=-\left(18\mathrm{m}\right)\left(\cos 33.0掳\right) \\ =-15.09\mathrm{m} \end{gathered}$$

The resultant magnitude of the winner in the x direction is given by,

$R_x=A_x+B_x+C_x$

Substituting the values in the above equation,

$$\begin{gathered} R_x=0+38.0\mathrm{m}+\left(-9.80\mathrm{m}\right) \\ =28.2\mathrm{m} \end{gathered}$$

The resultant magnitude of the winner in the y direction is given by,

$R_y=A_y+B_y+C_y$

Substituting the values in the above equation,

$$\begin{gathered} R_y=\left(20.8\mathrm{m}\right)+0+\left(-15.09\mathrm{m}\right) \\ =5.7\mathrm{m} \end{gathered}$$

The equation of the resultant vector is expressed as,

$R=\sqrt{R_x^2+R_y^2}$

Here, R is the resultant vector

Substituting the values in the above equation,

$$\begin{gathered} R=\sqrt{{\left(28.2\mathrm{m}\right)}^2+\left(5.7\mathrm{m}\right)} \\ =28.8\mathrm{m} \end{gathered}$$

Thus, the winner will have to travel$R=28.8\mathrm{m}$to cover shortest distance.

The equation of the direction of the winner is given by,

$\tan 胃=\frac{R_y}{R_x}$

Here,$\tan 胃$is the angle of the direction of the winner

Substituting the values in the above equation,

$$\begin{gathered} \tan 胃=\frac{5.70\mathrm{km}}{28.2\mathrm{km}} \\ \mathrm{胃}={\tan }^{-1}\left(\frac{5.70\mathrm{km}}{28.2\mathrm{km}}\right) \end{gathered}$$

Thus, the winner will travel$11.4掳\mathrm{north}鈥�\mathrm{east}$.