What is the speed of the waves on the lake?

[Foxhound101]

Homework Statement

While anchored in the middle of a lake, you count exactly three waves hitting your boat every 12.0 s. You raise anchor and start motoring slowly in the same direction the waves are going. When traveling at 1.50 m/s, you notice that exactly two waves are hitting the boat from behind every 12.0 s.

What is the speed of the waves on the lake?

Homework Equations

f_+-=(1+-v₀/v)f₀

The Attempt at a Solution

I have messed up this kind of problem before, so there are many places for me to make mistakes.

3 waves 12 seconds
V= 1.5m/s
2 waves 12 seconds

T₁ = 4s
T₂ = 6s

f₁=.25
f₂=.17

.17=(1-v₀/1.5).25

.68=1-v₀
-.32=-v₀/1.5
.48=v₀

I know I made a mistake somewhere...

 

[Gear300]

You got the overall idea for the equations but you made a slight mistake...1.5 m/s is the value of Vo (the object's velocity) and v is the velocity of the wave. You mixed the two up.

 

[Foxhound101]

Thank you, that was the mistake.