Answer:
The value is [tex]h = 32.91 \ m[/tex]
Explanation:
From the question we are told that
The diameter of each wheel is [tex]d = 52 \ cm = 0.52 \ m[/tex]
The mass of the motorcycle is [tex]m = 320 \ kg[/tex]
The rotational kinetic inertia is [tex]I = 2.1 \ kg \ m^2[/tex]
The mass of the rider is [tex]m_r = 75 \ kg[/tex]
The velocity is [tex]v = 85 \ km/hr = 23.61 \ m/s[/tex]
Generally the radius of the wheel is mathematically represented as
[tex]r = \frac{d}{2}[/tex]
=> [tex]r = \frac{0.52}{2}[/tex]
=> [tex]r = 0.26 \ m[/tex]
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
=> [tex]Mgh = \frac{1}{2} Mv^2 + \frac{1}{2} Iw^2 + \frac{1}{2} Iw^2[/tex]
=> [tex]Mgh = \frac{1}{2} * Mv^2 + Iw^2[/tex]
Here [tex]w[/tex] is the angular velocity which is mathematically represented as
[tex]w = \frac{v }{r }[/tex]
So
[tex]Mgh = \frac{1}{2} * Mv^2 + I \frac{v}{r} ^2[/tex]
Here [tex]M = m_r + m[/tex]
[tex]M = 320 + 75[/tex]
[tex]M = 395 \ kg[/tex]
[tex]395 * 9.8 * h = 0.5 * 395 * (23.61)^2 + 2.1 *[\frac{ 23.61}{ 0.26} ] ^2[/tex]
=> [tex]h = 32.91 \ m[/tex]
