A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surfac
e of the water. It takes a time of 2.30 ss for the boat to travel from its highest point to its lowest, a total distance of 0.650 mm. The fisherman sees that the wave crests are spaced a horizontal distance of 6.10 mm apart. (a) How much is the wavelength? Express your answer using three significant figures.
(b) Find the period of the wave. Express your answer using three significant figures.
(c) How fast are the waves traveling? Express the speed v in meters per second using three significant figures.
(d) What is the amplitude A of each wave? Express your answer in meters using three significant figures.
a) The wave length is the distance between 2 crests λ = 6.1m
b) The period of the wave is the time it takes from the lowest point to the next lowest point, which is twice the time it takes from the lowest point to the highest point = 2*2.3 = 4.6 s
c) The speed of the wave is the distance per unit of time, or wave length over period = 6.1 / 4.6 = 1.326 m/s
d)The amplitude A is half the distance from the highest point to the lowest point = 0.65 / 2 = 0.325 m
we assume the acceleration is constant. we choose the initial and final points 1.40s apart, bracketing the slowing-down process. then we have a straightforward problem about a particle under constant acceleration. the initial velocity is v xi =632mi/h=632mi/h( 1mi 1609m )( 3600s 1h )=282m/s (a) taking v xf =v xi +a x t with v xf =0 a x = t v xf −v xf = 1.40s 0−282m/s =−202m/s 2 this has a magnitude of approximately 20g (b) similarly x f −x i = 2 1 (v xi +v xf )t= 2 1 (282m/s+0)(1.40s)=198m
