Final answer:
The speed at which the snowboarder launched from the rim of the half-pipe can be calculated using conservation of energy or kinematic equations, leading to the use of the formula √(2 × g × h), where g is the acceleration due to gravity (9.81 m/s²) and h is the height (5.6 m).
Step-by-step explanation:
The question involves finding the launch speed of a snowboarder who rose 5.6 m above the rim of the half-pipe during the 2014 Olympic games. To solve for this speed, we can use the principles of conservation of energy or kinematics.
One approach is to use the conservation of energy, where the snowboarder's initial kinetic energy is completely converted into potential energy at the apex of his trajectory. We can calculate the snowboarder's initial kinetic energy (KE) using the formula KE = m × g × h, where m is the snowboarder's mass, g is the acceleration due to gravity (9.81 m/s²), and h is the height (5.6 m).
Alternatively, we can use the kinematic equations. The vertical speed (v) necessary to reach a height (h) can be found using the equation v = √(2 × g × h), where g is the acceleration due to gravity. This gives us the vertical component of the velocity at the moment of leaving the rim. If air resistance can be neglected and no additional forces are acting on the snowboarder, this speed will be the same as the launch speed.
Note that additional information, such as the mass of the snowboarder or their horizontal speed, is not required for these calculations as they don't affect the ascent in vertical motion for this energy conservation approach or the kinematic calculation for vertical motion.