A transverse wave on a long horizontal rope with a
wavelength of 8 m travels at 2 m/s. At t= 0, a
particular point on the rope has a vertical
displacement of +A, where A is the amplitude of
the wave. At what time will the vertical
displacement of this same point on the rope be -A ?

The time taken by the wave to travel the vertical  displacement from the point on the rope to -A is 2 seconds

Given to us:

wavelength λ = 8 m,

Velocity v = 2 m/s,

The frequency of a wave is given by:

Therefore, the frequency of the wave is 0.25 Hz.

The period of a wave is equal to the reciprocal of the frequency,

Therefore, It takes 4 seconds to complete one full cycle.

Hence, the time taken by the wave to travel the vertical  displacement from the point on the rope to -A is 2 seconds as its is the half distance which is needed to be traveled by the wave.  

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2 seconds

Explanation:

The frequency of a wave is related to its wavelength and  speed by the equation

where

f is the frequency

v is the speed of the wave

is the wavelength

For the wave in this problem,

v = 2 m/s

So the frequency is

The period of a wave is equal to the reciprocal of the frequency, so for this wave:

This means that the wave takes 4 seconds to complete one full cycle.

Therefore, the time taken for the wave to go from a point with displacement +A to a point with displacement -A is half the period, therefore for this wave:

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards