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

Solution :

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

$\frac{dL}{dt}+2\frac{da}{dt}=\frac{dC}{dt}$  

$\frac{dL}{dt}=V_T = 18 \ ft/s$          

$18 + 2 \frac{da}{dt}=0$

where, $\frac{da}{dt} = V_C =$    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