Each wheel of a 320 kg motorcycle is 52 cm in diameter and has rotational inertia 2.1 kg m2 . The cycle and its 75 kg rider are coasting at 85 km/h on a flat road when they encounter a hill. If the cycle rolls up the hill with no applied power and no significant internal friction, what vertical height will it reach

The value is  

Explanation:

From the question we are told that

    The diameter of each wheel is  

    The mass of the motorcycle is  

    The rotational kinetic inertia is  

    The  mass of the  rider is  

     The  velocity is  

      Generally the radius of the wheel is mathematically represented as

=>    

=>    

Generally from the law of energy conservation

     Potential energy  attained  by  system(motorcycle and rider )  =  Kinetic  energy of the system  +  rotational kinetic energy of  both wheels of the motorcycle

=>  

=>    

Here   is the angular velocity which is mathematically represented as

So

Here

=>  

r = ρ x length / area  

ρ = r x area / length  

ρ is in ohm-meters  

in basic units, it is m³kg/s³a²  

i think this is it.