Final 11 - Dead Reckoning

Given:

• $\mbox{A ship travels:}$
• $\mbox{East at 12 km/hour for 2 hours}$
• $\mbox{Then south at 20 km/hour for 1 hour}$
• $\mbox{Then east at 15 km/hour for 3 hours}$
• $\mbox{Then northeast into port at 8 km/hour for 1 hour.}$

Question:

• $\mbox{What is the straight line distance traveled to port ? }$

Rationale:

• $\mbox{Segment-distance}  = velocity * time$
• $East_{distance} = \Delta{x}$
• $South_{distance} = \Delta{y}$
• $-\Delta{y_{northeast} = \Delta{x_{northeast}} = \sin{45^{\circ}}} * Northeast_{distance}$
• $\mbox{Straight-line-distance} = \sqrt{(\Delta_{x-total})^2 + (\Delta_{y-total})^2 }$

Calculate:

• $East_{distance} = ((12) (2.5)) + ((15) (3)) =  75$
• $South_{distance} = (20) (1) = 20$
• $-\Delta{y_{northeast}}  = \Delta{x_{northeast}} = (0.707106781) (8) (1) = 5.656854$
• $\Delta_{x} = 75 +  5.656854 = 80.656854$
• $\Delta_{y} = 20 - 5.656854 = 14.343146$
• $\mbox{Straight-line-distance} = \sqrt{(80.656854)^2 + (14.343146)^2}$
• $\mbox{Straight-line-distance} = \sqrt{(6505.5280 + 205.7258 )} = \sqrt{6711.2538}$
• $\mbox{Straight-line-distance} =81.9222 \approx 81.9$

References: