Astanding wave is established on a string that is fixed at both ends. if the string is vibrating at its fundamental frequency, how is the length of the string related to the wavelength of the standing wave? the length of the string is equal to one-half of a wavelength. the length of the string is equal to twice the wavelength. the length of the string is equal to four times the wavelength. the length of the sting is equal to one-quarter of a wavelength. the length of the string is equal to the wavelength.

Option A

The length of the string is equal to one-half of a wavelength

Explanation:

standing wave is established on a string that is fixed at both ends. If the string is vibrating at its fundamental frequency, how is the length of the string related to the wavelength of the standing wave? The length of the string is equal to one-half of a wavelength. The length of the string is equal to twice the wavelength. The length of the string is equal to four times the wavelength. The length of the sting is equal to one-quarter of a wavelength. The length of the string is equal to the wavelength.

the velocity you are looking for is made up of two parts: horizontally velocity, vh, and its vertical velocity, vv. the actual velocity of the ball will be these two parts added together, and because velocity is a vector then they will need to be added vectorially.  

neglecting air resistance etc etc.,  

the horizontal velocity component will be constant (because there is no accelerating force in the horizontal direction.  

vh = 8 ms-1  

the vertical velocity component has an accelerating force: 'g'.  

using v = u +at where a = g = 9.81 ms-2.  

the vertical component of velocity, vv = 0 + gt = vv =9.81 x 2  

vv = 19.62 ms-1 . the zero appears because the virtical component of velocity at time t=0 is zero. remember, the ball was thrown horizontally.  

how fast it will be moving (it actual path (being a parabola )) will be the vector sum of these two.  

adding vectorally gives: -  

v = sqr root (8^2 + 19.62^2) = sqr root(64+384.9) = 21.18 or 21.2 ms-1

car a and b are moving in opposite directions

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