Final answer:
To determine the height the motorcycle can coast up the hill, we can use the principle of conservation of mechanical energy. When neglecting friction, the initial mechanical energy of the motorcycle will be equal to its final mechanical energy at the highest point of the hill. The motorcycle can coast up the hill to a height of approximately 289.8 meters.
Step-by-step explanation:
To determine how high the motorcycle can coast up the hill, we can use the principle of conservation of mechanical energy. When neglecting friction, the initial mechanical energy of the motorcycle will be equal to its final mechanical energy at the highest point of the hill.
The initial mechanical energy consists of the kinetic energy of the motorcycle and the potential energy of the motorcycle at the bottom of the hill, while the final mechanical energy only consists of the potential energy of the motorcycle at the highest point of the hill.
The kinetic energy of the motorcycle can be calculated using the formula: KE = (1/2)mv^2, where m is the mass of the motorcycle and v is its speed.
The potential energy of the motorcycle can be calculated using the formula: PE = mgh, where m is the mass of the motorcycle, g is the acceleration due to gravity, and h is the height. Equating the initial mechanical energy to the final mechanical energy, we can solve for the height h:
KE + PE = PE
(1/2)mv^2 + mgh_start = mgh_end
Simplifying the equation, we find:
h_end = (1/2)v^2/g + h_start
Substituting the given values, we have:
h_end = (1/2)(34 m/s)^2/9.8 m/s^2 + 0 m
h_end = 289.8 m
Therefore, the motorcycle can coast up the hill to a height of approximately 289.8 meters when neglecting friction.