Solving a River Boat Problem: Distance Downstream

[blayman5]

Homework Statement

A river flows due North at 3.17 m/s. A boat
crosses the river from the West shore to the
East shore by maintaining a constant velocity
of 8.5 m/s due East relative to the water.
If the river is 163 m wide, how far downstream
is the boat when it reaches the East shore?
Answer in units of m




The attempt at a solution
I found the magnitude of velocity which was 9.7187 and its direction.
I used the law of motion
y)163=3.17sin(90)t+4.9t^2
to solve for x) x=8.5cos(0)(time i got for y)+4.9(time i got for y^2)
Am I going about this the right way?

 

[tiny-tim]

Hi blayman5!

I found the magnitude of velocity which was 9.7187 and its direction.

hmm … I make it 9.07187.

I used the law of motion
y)163=3.17sin(90)t+4.9t^2
to solve for x) x=8.5cos(0)(time i got for y)+4.9(time i got for y^2)
Am I going about this the right way?

Nooo … that looks like an accelerated motion equation.

i] This is uniform motion

ii] You don't need to find the time …

you know the direction from the first part … so just use geometry!

 

[blayman5]

So use the magnitude of velocity and direction along with the water velocity and solve for the x side?

 

[blayman5]

i get it

tanx=length/width
width*tanX=length

163*tan(20.4526)=60.7896
thanks