A fisherman notices that his boat is moving up and down periodically, owing to w

Question

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 2.70s for the boat to travel from its highest point to its lowest, a total distance of 0.640m . The fisherman sees that the wave crests are spaced 6.20m apart.

Part A

How fast are the waves traveling?

Part B

What is the amplitude of each wave?

Part C

If the total vertical distance traveled by the boat were 0.500m , but the other data remained the same, how fast are the waves traveling ?

Part D

If the total vertical distance traveled by the boat were 0.500m , but the other data remained the same, what is the amplitude of each wave?

Explanation / Answer

the time taken to travel from its highest point to lowest is

t1=2.7sec

then time taken to travel one complite full wave is time period

T=2*2.7=5.4 sec

frequency f=1/T =1/5.4

=0.18 Hz

w=2pi/T

=2*3.14/5.4

=1.163 rad/sec

and

distance travelled d1=0.64 m

then

wave length lambda=6.2 m

A)

wave velocity v=f*lambda

=0.18*6.2

=1.12 m/sec

b)

v=A*w

1.12=A*1.163

===>

A=0.963 m

C)

v=w*sqrt(A^2-x^2)

=1.163*sqrt(0.963^2-0.5^2)

=0.957 m/sec

D)

v=A*w

0.957=A*1.163

A=0.823 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.