Math: Calculus  Vectors
posted by Anonymous
A boat travels at a speed of 5 m/s in still water. The boat moves directly across a river that is 70m wide. The water in the river flows at a speed of 2 m/s. How long does it take the boat to cross the river? In what direction is the boat headed when it starts the crossing.
Textbook Answer: 15.3 m/s, 66.4 degrees to shore
My answer: 14 seconds and 22 degrees from the shore.
This is what I did: I found the speed of the resultant by doing the Pythagorean (5.4 m/s),then found the distance of the resultant by "5/70 = 2/x (28m)" and then using the Pythagorean (75.4m), and then I found the time by doing "t = d/s". Then, I found the direction of the boat by using trig, "tanx = 2/5"
MY QUESTION: What did I do wrong? And can you please help me fix my mistake?

drwls
How can the textbook answer be 15.3 m/s if they are asking for the crossing time?
To go directly across, the boat must aim upstream so that the velocity component upstream relative to the water is 2 m/s. That makes its velocity component across the water sqrt[5^2  2^2) = sqrt 21 = 4.58 m/s. The crossing time is
70 m/4.58 m/s = 15.3 s. The pointing angle of the boat is cos^1 4.58/5 = 23.7 degrees relative to the crossstream direction, or 66.3 degrees relative to the shore. 
Quidditch
If the boat moves directly across then there is enough of the boats speed vector to counteract the river flow. That is 2m/s.
So, the vector parallel to the shore (the river flow) speed is 2m/s. The TOTAL speed of the boat is 5m/s. Now solve this for the speed perpendicular to the shore.
SQRT(5^2  2^2).
Divide that into the distance (70m).
Use any of the trig values to find the angle.
Respond to this Question
Similar Questions

physics
A boat crosses a river, which is 60 meters wide in 15 seconds. Upon crossing, the boat, which had headed straight across the river, ended up 20 meters downstream. A). What was the speed of the boat in still water? 
Physics
A boat travels at 3.8 m/s and heads straight across a river 240m wide at an angle of 145'. The river flows at 1.6 m/s. a. What is the boat's resultant speed with respect to the river bank? 
Physics
A boat travels at 3.8 m/s and heads straight across a river 240m wide at an angle of 145'. The river flows at 1.6 m/s. a. What is the boat's resultant speed with respect to the river bank? 
Physics
A boat travels at 3.8 m/s and heads straight across a river 240m wide at an angle of 145'. The river flows at 1.6 m/s. a. What is the boat's resultant speed with respect to the river bank? 
physics
A boat propelled so as to travel with a speed of 0.50m/s in still water, moves directly (in a straight line) across a river that is 60m wide. The river flows with a speed of 0.30m/s. How long in seconds does it take the boat to cross … 
Advanced Maths (Vectors) AQA Level, please help?
A boat which can travel at 5m/s in still water is crossing a river 200 m wide.the rate of the flow of the river is 2 m/s assumed uniform at every point in the river. Point A and B are directly opposite to each other across the river. … 
Advanced Maths (Vectors) AQA Level
A boat which can travel at 5m/s in still water is crossing a river 200 m wide.the rate of the flow of the river is 2 m/s assumed uniform at every point in the river. Point A and B are directly opposite to each other across the river. … 
math
20. Miguel is driving his motorboat across a river. The speed of the boat in still water is 11 mi/h. The river flows directly south at 2 mi/h. If Miguel heads directly west, what are the boatâ€™s resultant speed and direction? 
math
The speed of a powerboat in still water is 35 mi/h. It is traveling on a river that flows directly south at 8 mi/h.the boat heads directly west across the river. What are the resulting speed and direction of the boat? 
Physics
A boat propelled so as to travel with a speed of 0.5m/s in still water, moves directly (in a straight line) across a river that is 60m wide. The river flows with a speed of 0.30m/s. How long in seconds does it take the boat to cross …