Posted by **jhon** on Thursday, August 16, 2012 at 2:58am.

A motorboat travels due north at a steady speed of 3.0 m/s through calm water in which there is no current. The boat then enters an area of water in which a steady current flows at 2.0 m/s in a southwest direction, as shown in the next picture. Both the engine power and the course setting remain unchanged.

a) explain how the above paragraph gives information not only about the speed of the boat but also about its velocity.

b) draw a vector diagram showing the velocity of the boat and the velocity of the current. Use the diagram to find

i) the magnitude of the resultant velocity

ii) the angle between due north and the direction of travel of the boat.

c) calculate the distance the boat now travels in 5 mins;

d) mass of boat is 3.0 x 103kg (3000kg). Calculate the additional force that needs to be applied to give the boat an initial acceleration of 2.5 x 10-2m/s2 (0.025 m/s2).

- physics -
**Henry**, Thursday, August 16, 2012 at 7:40pm
a. When both speed and direction are

given, we call it velocity.

b. Draw a vector from the origin

pointihg due north to represent the velocity of the boat

Draw a vector from the origin 45o South of West(225o) to represent the velocity of the current.

1. Vr = 3m/s @ 90o + 2m/s @ 225o = Resultant velocity.

X = Hor. = 2*cos225 = -1.414 m/s.

Y = Ver. = 3 + 2*sin225 = -1.586 m/s.

(Vr)^2 = X^2 + Y^2 = 2 + 2.5 = 4.5

Vr = 2.12 m/s. = Resultant velocity.

2. cosA= X/Vr=-1.586 / 2.12 = -0.66708

A = 132o. = Direction of travel of boat.

132 - 90 = 42o Between North and direction of travel of boat.

c. 5min. = 300 s.

d = Vr*t = 2.12m/s * 300s = 636 m.

3.

## Answer this Question

## Related Questions

- algebra - a motorboat travels 22 mph with the current and 8 mph against the ...
- Physics - The swim portion of a triathlon takes place in a river and is an out-...
- algebra - A motorboat traveling a distance of 225 miles in 5 hours while ...
- Precalc - A boat that travels at 16 knots in calm water is sailing across a ...
- physics - A boat must head due north across a river channel that has a current ...
- math - a motorboat traveling with the curent went 68 miles in 3hrs and 24mins. ...
- Physics - You have a boat that is capable of moving at 14.5 m/s through still ...
- Math - It took a boat 6 h to travel 84 km up a river against the current but ...
- physics - 1. A ship has a top speed of 3.0 m/s in calm water. The current of the...
- algebra - A boat can travel 59 mph in still water. If it travels 325 miles with...