Crossing the rapids . An east-west-running river is 25.0 m wide, and you are try

Question

Crossing the rapids. An east-west-running river is 25.0 m wide, and you are trying to cross it from the south shore to the north shore. Working your engine at maximum power, your boat can accelerate at a constant 2.50 m/s^2 relative to stationary water. However, it is not stationary: it is flowing eastward at a constant speed of 12.5 m/s; so it will take longer to cross and you will land at a distance D farther east,

(A) In unit-vector notation, write down your acceleration and your initial velocity, relative to the shore.

(B) Calculate the time it takes for you to cross the river, assuming constant acceleration.

(C) Calculate D

(D) Find the final speed and direction of your motion just before you hit the north shore.

Explanation / Answer

A) intial velocity vector = -12.5 m/sec i^

acceleration = 2.5 m/sec2 j^

B) distance s = 25 m

acceleration a = 2.5 m/sec2

initial veloctity along y direction = 0

s = ut + 0.5 * a * t^2

25 = 0 + 0.5 * 2.5 * t^2

so time taken = t = sqrt (25 *2 / 2.5) = 4.472 secs

C) so drift = time * speed of water = 4.472 * 12.5 = 55.9 m

D = 55.9m away

D) velocity along x = -12.5 m/sec

velocity along y = 2.5*4.472 =11.18 m/sec

so speed = sqrt ( 11.18^2 + 12.5^2 ) = 16.77 m/sec

direction = tan inverse ( 12.5 /11.18 ) = 48.19 degree west of north

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