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Chap 3 Questions.. PLease HELP>>>

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Question:

A river flows due south with a speed of 2.00 ${\rm m}/{\rm s}$ . A man steers a motorboat across the river; his velocity relative to the water is 4.20 ${\rm m}/{\rm s}$ due east. The river is 800 ${\rm m}$ wide.

Part A:What is the magnitude of his velocity relative to the earth?
Part B: What is the direction of his velocity relative to the earth?
Part C: How much time is required for the man to cross the river?
Part D: How far south of his starting point will he reach the opposite bank?

I am stuck please help me out..

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Answers:

Eridani 2

Mentor

Karma Points: 422

Date Posted: 7/2/2008 7:48:52 PM Status: Live

Asker's Rating: Somewhat Helpful

Response:

The boat is going 4m/s sideways AND 2 m/s downward at the same time.

A) To find net velocity, use pythagorean theorem v = √[(2²) + (4²)] = √20

B) To find the direction as a vector, just use the components you were given:

v = 4i - 2 j

C) Time = Distance / Velocity using only the x components. (No conversions necessary since all units are in meters and seconds.

t = 800 m / (4.2 m/s) = 190 sec

D) Using the same equation as above, Distance = Time * Velocity, this time using only the y components since we're looking for distance downstream.

y = 190 sec * (2 m/sec) = 380 m

12345687155's Comment:

Answers A and B are wrong!

12345687155

Scholar

Karma Points: 306

Date Posted: 7/2/2008 8:26:43 PM Status: Live

Asker's Rating: N/A-Posted by Person Asking Question

Response:

I still cant figure out how to do part A and B? Anyone out there help??

zsm28

Oracle

Karma Points: 14,581

Date Posted: 7/2/2008 8:37:18 PM Status: Live

Asker's Rating: Lifesaver

Response:

velocity of water v_w = 2.00 m/s (S)
velocity of man relative to water v_m/w = 4.20 m/s (E)
a) velocity of man v = vector sum of v_w and v_m/w,
magnitude of v = √(v_w² + v_m/w²) = 4.65 m/s
b) tanθ = 2.00/4.20 = 0.4762
θ = 25.5^o
direction: south of east 25.5^o
c) time t = 800 m/4.20 m/s = 190.5 s
d) d = 2.00 * t = 2.00 * 190.5 = 381 m

12345687155's Comment:

Thank I see how its done now.. Thanks..

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