Answer:
Explanation:
Given
inclination [tex]\theta =12^{\circ}[/tex]
Initial velocity of rock [tex]u=15\ m/s[/tex]
length of track [tex]s=2400\ m[/tex]
Theoretical speed of rock can be given by using
[tex]v^2-u^2=2as[/tex]
where v=final velocity
u=initial velocity
a=acceleration
s=displacement
here gravity sin component will accelerate the rock
[tex]a=g\sin 12[/tex]
[tex]v^2-(15)^2=2\times (g\sin (12))\cdot 2400[/tex]
[tex]v^2=225+9780.165[/tex]
[tex]v=\sqrt{10,005.165}[/tex]
[tex]v=100.025\ m/s[/tex]
It is given that velocity at the bottom is [tex]v=40\ m/s[/tex]
this is because of friction
According to work-energy theory Change in kinetic energy of an object is given by work done by all the forces
[tex]W_g+W_f=\Delta k[/tex]
where [tex]W_g[/tex]=gravity work
[tex]W_f[/tex]=Friction work
[tex]\Delta k[/tex]=change in kinetic Energy
[tex]W_g=mgh=m\cdot g\cdot 2400\sin 12[/tex]
[tex]W_g=mg\cdot =498.98mg[/tex]
[tex]W_f=f\cdot 2400[/tex]
[tex]\Delta k=0.5\cdot m(100.02^2-40^2)[/tex]
substituting values we get
[tex]f_{avg}=1.75 m[/tex]
where m is the mass of rock
