Question

Area of orifice is a. Due to ejection of water of density p at a constant speed, the equilibrium compression in spring is x. The speed of ejection of water is...

(Please answer ASAP !)

Answer 1

Thrust force due to ejection of water on the cart is counter balanced by spring force on the cart

so we can write

`F_t = v (dm)/(dt)`

here we have

`(dm)/(dt)` = rate of mass ejection

`(dm)/(dt) = \rho a(dx)/(dt) = \rho a v`

now from above formula

`F_t = \rho a v(v) = \rho av^2`

Now by force balance equation

`F_t = F_s`

`\rho a v^2 = kx`

by rearranging the terms now

`v= \sqrt{(kx)/(\rho a)}`