Thank you for visiting The car is stuck and is being pulled out by a wrecker truck If the truck is moving to the right with a velocity of. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
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
[tex]$\frac{dL}{dt}+2\frac{da}{dt}=\frac{dC}{dt}$[/tex]
[tex]$\frac{dL}{dt}=V_T = 18 \ ft/s$[/tex]
[tex]$18 + 2 \frac{da}{dt}=0$[/tex]
where, [tex]$\frac{da}{dt} = V_C = $[/tex] speed of the car
So
[tex]$18+2V_C=0$[/tex]
[tex]$V_C = -9 \ ft/s$[/tex] (only magnitude of speed has significance, so negative sign
is ignored )
Therefore, the speed of the car is 9 ft/s
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Rewritten by : Jeany
