Question

a truck rolling down a hill 500ft with coefficient of friction 0.02 and gradient 2.5, what is the speed of the truck

Answer 1

As per the given question,

Height of the inclined plane $(h)=500ft$

Coefficient of friction $(\mu)=0.02$

Gradient $(m)=\tan\theta=2.5$

$\Rightarrow \frac{height}{base}=2.5$

$\Rightarrow \frac{500}{base}=2.5$

$\Rightarrow base=\dfrac{500}{2.5}ft$

$\Rightarrow base=\frac{152.4}{2.5}m$

$\Rightarrow base=60.96m$

$\sin \theta=\frac{152.4}{164.13}=0.928$

$\cos\theta =\frac{60.96}{164.13}=0.37$

Let the resultant acceleration of the truck is $=a$

So, $a=g\sin\theta-\mu g\cos\theta$

$\Rightarrow a=9.8\times 0.92-0.02\times 9.8\times 0.37 m/sec^2$

$\Rightarrow a=8.943 m/sec^2$

$\Rightarrow v^2=u^2+2as$

$\Rightarrow v=\sqrt{2as}$

$\Rightarrow v=\sqrt{2\times 8.94\times 164.13}$

$\Rightarrow v=54.17m/sec$