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September 16, 2014

September 16, 2014

Posted by **Megan** on Sunday, September 8, 2013 at 12:04am.

(a) What is her speed with respect to the starting point on the bank?

(b) How long does it take her to cross the river?

(c) How far upstream or downstream from her starting point will she reach the opposite bank?

(d) In order to go straight across, what angle upstream should she have headed?

- physics -
**Graham**, Sunday, September 8, 2013 at 1:43amLet u : her speed across the stream

Let v : her speed up the stream

Find w : her speed relative to the bank

u = 3.13 cos(60°) [mi/h]

v = 3.13 sin(60°) - 1.35 [mi/h]

Her speed relative to the bank.

w = √(u^2+v^2)

w = √((3.13^2+(3.13√3-1.35)^2)/2) [mi/h]

Time to cross the stream:

Let x : the distance across the bank

Find t : the time to cross the stream

x = 1.10[mi]

t = x/u

t = 1.10/(3.13 cos(60°)) [hr]

Distance traveled up

Find y : the distance upstream

y = vt

y = 1.10(3.13 sin(60°)-1.35)/(3.13 cos(60°)) [mi]

Let θ : angle needed to travel straight across.

Ergo: to have a zero upstream velocity.

0 = 3.13 sin(θ) - 1.35

θ = arcsin(1.35/3.13)

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