Answer to Question #162201 in Physics for Ash

Question

1. In the World Pond Hockey tournament held in Plaster Rock, NB, a puck on the ice travels 20.0 m [25° W of N], gets deflected, and travels 30.0 m [35° N of W]. Determine where the puck will end up with respect to its starting point, e.g., the puck's total displacement, using the three different methods discussed.

Answer 1

The total displacement can be found if we find the x and y-components of the two vectors. Begin with the 20m-vector:

$$A_x=A\text{ sin}\theta_A=20\text{ sin}25°=8.45\text{ m},\\ A_y=A\text{ cos}\theta_A=20\text{ cos}25°=18.1\text{ m}.$$

Repeat the calculations for the second vector:

$$B_x=B\text{ sin}\theta_B=30\text{ cos}35°=24.6\text{ m},\\ B_y=B\text{ cos}\theta_B=30\text{ sin}35°=17.2\text{ m}.$$

Calculate the resultant:

$$R_x=A_x+B_x,\\ R_y=A_y+B_y,\\ R=\sqrt{R_x^2+R_y^2}=\\=\sqrt{(A_x+B_x)^2+(A_y+B_y)^2}=48.4\text{ m}.$$

The angle (N of W) is

$$\theta=\text{atan}\frac{R_y}{R_x}=46.9°.$$