review the diagram. a laser beam is aimed 25° from horizontal at a mirror 120 m away. the beam bounces off…

Explanation:

Step1: Resolve vectors into components

Let the first - stage displacement be $\vec{d_1}$ with magnitude $d_1 = 120$ m and angle $\theta_1=25^{\circ}$ above the horizontal, and the second - stage displacement be $\vec{d_2}$ with magnitude $d_2 = 90$ m and angle $\theta_2 = 20^{\circ}$ above the horizontal. The $x$ - components of the displacements are: $d_{1x}=d_1\cos\theta_1=120\cos(25^{\circ})\approx120\times0.9063 = 108.756$ m $d_{2x}=d_2\cos\theta_2=90\cos(20^{\circ})\approx90\times0.9397 = 84.573$ m The $y$ - components of the displacements are: $d_{1y}=d_1\sin\theta_1=120\sin(25^{\circ})\approx120\times0.4226 = 50.712$ m $d_{2y}=d_2\sin\theta_2=90\sin(20^{\circ})\approx90\times0.3420 = 30.78$ m

Step2: Calculate the total $x$ and $y$ components

The total $x$ - component of the displacement $\vec{D}$ is $D_x=d_{1x}+d_{2x}\approx108.756 + 84.573=193.329$ m The total $y$ - component of the displacement $\vec{D}$ is $D_y=d_{1y}+d_{2y}\approx50.712+30.78 = 81.492$ m

Step3: Use the Pythagorean theorem

The magnitude of the displacement $D$ from the origin to the final point is given by $D=\sqrt{D_x^{2}+D_y^{2}}$ $D=\sqrt{(193.329)^{2}+(81.492)^{2}}=\sqrt{37376.47 + 6641.97}=\sqrt{44018.44}\approx194$ m

Answer:

approximately 194 m