Question

The car is stuck and is being pulled out by the wrecker truck. If the truck is moving to the right with a velocity of 18 ft/s, what is the velocity of the car?'

Answer 1

Assume that the length of the string is constant and the string is inextensible.

The length of the string between the truck and pulley 1 is constant. Also total length of string connecting the truck wrapping pulley 1 and passing over pulley 2 is also constant.

Therefore, from the figure,

L+a+a = constant

L+2a = C

Differentiating both sides w.r.t time, we get

`$(dL)/(dt)+2(da)/(dt)=(dC)/(dt)$`

`$(dL)/(dt)=V_T = 18 \ ft/s$`

`$18 + 2 (da)/(dt)=0$`

where,
`$(da)/(dt) = V_C = $` speed of the car

So

`$18+2V_C=0$`

`$V_C = -9 \ ft/s$` (only magnitude of speed has significance, so negative sign

is ignored )

Therefore, the speed of the car is 9 ft/s