A small rocket-propelled test vehicle with a total mass of 100 kg starts from re

Question

A small rocket-propelled test vehicle with a total mass of 100 kg starts from rest at A and moves with negligible friction along the track in the vertical plane as shown. If the propelling rocket exerts a constant thrust T of 1.5 kN from A to B where it is shut off. Determine the distance s which the vehicle rolls up the incline before stopping. Radius of curvature is 120m, angle between A and B is 30o. The path is straight at B.

A small rocket-propelled test vehicle with a total mass of 100 kg starts from rest at A and moves with negligible friction along the track in the vertical plane as shown. If the propelling rocket exerts a constant thrust T of 1.5 kN from A to B where it is shut off. Determine the distance s which the vehicle rolls up the incline before stopping. Radius of curvature is 120m, angle between A and B is 30 degree. The path is straight at B.

Explanation / Answer

Now T=centripital force+inetial force due to tangeantial acceleartion

at=v^2/2*s

=v^2/2*(pi/6*120)

=v^2/20*pi

so T=mv^2/r+m*at

1.5*10^3=100*(v^2/120+v^2/20*pi

v=24.87 m/s at Point B

B makes 60 degree with horizontal so we have

Vv=Vsin(60)=21.54 m/s and Vh=12.43 m/s

t=21.54/9.81

=2.19 s

so horizontal distance travelled

hh=12.43*2.19=27.3 m

and vertical distance

hv=21.54*2.19-1/2*9.81*2.19^2

=23.64 m

So total distance =sqrt(hh^2+hv^2)

=36.11 m ans

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