First, we need to convert the current speed from knots to mph.
6 knots * 1.15077945 mph/knot ≈ 6.904677 mph
Now, we can analyze the problem using vector addition. The components of the Criss Craft Racing Runabout boat and the components of the current will add up to the components of the resulting motion of the boat relative to the shore.
Let the boat speed in the x-direction be Bx, and its speed in the y-direction be By. The current speed in the x-direction is Cx = 0 (since it's in the southward direction), and the current speed in the y-direction is Cy = -6.904677 mph (negative y-direction).
The destination has an angle of S48°E, which means it forms a 48-degree angle with the y-axis in the southeast quadrant. We can relate the boat's x and y components to its speed using trigonometric functions.
Bx = boat speed * cos(90 - 48)°
Bx = 52 mph * cos(42)°
Bx ≈ 39.20 mph
By = boat speed * sin(90 - 48)°
By = 52 mph * sin(42)°
By ≈ 34.55 mph
Now, we can add the boat's components and the current's components to find the components of the boat's motion.
Rx = Bx + Cx = 39.20 mph
Ry = By + Cy = 34.55 mph - 6.904677 mph ≈ 27.65 mph
We can now find the resultant speed and the angle of the boat's motion.
Resultant speed = √(Rx^2 + Ry^2) ≈ √(39.20^2 + 27.65^2) ≈ 47.67 mph
Theta = arctan(Ry / Rx) ≈ arctan(27.65 / 39.20) ≈ 34.89°
Since the speed is in the southeast quadrant, the compass reading for the boat should be S(90 - 34.89)°E ≈ S55.11°E
The boat is actually traveling at around 47.67 mph relative to the shore.
Now, we can determine the time it will take to reach its destination
time = distance / speed = 50 miles / 47.67 mph ≈ 1.049 hours or approximately 1 hour and 3 minutes.
A Criss Craft Racing Runabout boat can travel at speeds up to 52 mph relative to the water. The boat is trying to reach a destination on a river that is S48°E of its point of departure. If the current is traveling at 6 knots in a southward direction, what compass reading should the boat maintain to reach its destination? How fast is the boat actually traveling relative to the shore? Also, if the destination is 50 miles from the point of departure, how long will it take the boat to reach its destination? (1 knot =1.15077945 mph).
1 answer