rest and motion 36

Q 36. Figure shows a 11.7 ft wide ditch, with the approach roads at an angle of 15° with the horizontal. With what minimum speed should a motorbike be moving on the road so that it safely crosses the ditch?

Assume that the length of the bike is 5 ft, and it leaves the road when the front part runs out of the approach road.

assume bike to be a point object and the length of the ditch be 2.5 + 2.5=0.5feet more wide that is 16.7ft wide because its given that it leaves the road when front part runs out the approach road!!!

then apply concept of projectile to determine the minimum speed with angle of projection being 15 degrees and range being 16.7 feets.



Please see diagram enclosed.









The center of mass of motor bike is C and it is in the shown position just before it is supposed to have taken off.  C' is the position when the bike lands safely ie., the rear part B must land on the road on the other side.

CC' is the range for the flight of the bike.  CC' = R
                   = 11.7' + 2.5' cos 15° + 2.5' Cos 15° = 16.53'

We assume that the angle of projection of center of mass is 15°.

Range for a two dimensional projectile : R = u² Sin 2Ф / g  = u² Sin (2*15°) / g
 
          u = √(2 R g ) = √(2*16.53 * 9.8 / 0.3048) = 32.6 feet / sec

This is a simple answer, we do not consider some other factors like rotation about center of mass, friction etc.

DITCH

MEANING

खाई

assume bike to be a point object and the length of the ditch be 2.5 + 2.5=0.5feet more wide that is 16.7ft wide because its given that it leaves the road when front part runs out the approach road!!!

then apply concept of projectile to determine tha minimum speed with angle of projection being 15 degrees and range being 16.7 feets.