Precalc
posted by Natalie .
A boat that travels at 16 knots in calm water is sailing across a current of 3 knots on a river 250 m wide. The boat makes an angle of 35 degrees with the current heading into the current.
Find the resultant velocity of the boat. How far upstream is the boat when it reaches the other shore?
Do I need to use parametric equations to solve this? If so, how do I find the time? Thanks in advance.

Precalc 
Damon
Boat velocity component upstream = 16 cos 35  3
= 13.1  3
= 10.1 kn
Boat velocity component across stream = 16 sin 35 = 9.18 kn
resultant speed = sqrt(10.1^2+9.18^2) = 13.6 kn
tangent of resultant angle to upstream = 9.18/10.1 = .909
so angle to upstream = tan^1 .909 = 42.3 deg
Now you do not have to know time T because
distance upstream = 10.1 T
distance across = 9.18 T
distance upstream/distance across =10.1/9.18 (The T cancels
so
10.1/9.18 = distance upstream/250 meters
so
distance upstream = 250 * 10.1/9.18 = 275 meters
That avoids having to convert nautical miles to meters. I suppose in a sense my use of T implies parametric :)
Respond to this Question
Similar Questions

maths please check
a yacht is sailing at a speed of 12 knots due south in calm water. if the tacht encounters a current of 4 knots from bearing 040 degrees: determine the resultant speed and direction of the yacht. here is my answers: 15.28 knots from … 
Calculus
A boat crosses a river and arrives at a point on the opposite bank directly across from its starting position. The boat travels at 4 m/s and the current is 2m/s. If the river is 600 m wide in what direction must the boat steer and … 
science
A boat crossing a .2 mile wide river is heading perpendicularly relative to shore. Its speed in still water is 4mph and the speed of the current is 6mp. a.) How far downstream will the boat land? 
PreCal
A pilot wishes to fly on course 290 with an air speed of 300 knots when the wind blows from 224 at 18 knots. Find the drift angle to the nearest hundredth of a degree. A.3.22° B.5.07° C.86.86° A river is flowing at the rate of 2.4 … 
Physics
A boater wants to head straight across a river that has a current of 3km/hr. If the top speed of the boat in still water is 4km/hr, find the direction the boat must travel into the current to go straight across the river. How fast … 
physics
A child in danger of drowning in a river is being carried downstream by a current that has a speed of 2.10 km/h. The child is 0.600 km from shore and 0.800 km upstream of a boat landing when a rescue boat sets out. (a) If the boat … 
Physics
A boat travels across a wide river. if the boat can travel at a speed of 25 mph and its pilot heads in a direction of 30 degrees, while the current's velocity is 5.1 mph at a heading of 270 degrees, what will the final velocity of … 
Math
A boat pilot wishes to go in a straight line across a river from the east dock to the west dock in a ferryboat that has a still water speed 8.0 knots. If the river has a Southward current of 2.5 knots, what compass heading should be … 
math
A boat pilot wishes to go in a straight line across a river from the east dock to the west dock in a ferryboat that has a still water speed 8.0 knots. If the river has a Southward current of 2.5 knots, what compass heading should be … 
physics
A boater wants to head straight across a river that has a current of 3 km/hr. If the top speed of the boat in still water is 4 km/hr. 1.find the direction the boat must travel into the current to go straight across the river?