Final answer:
To calculate the skater's initial horizontal velocity, we can use the concept of projectile motion. The horizontal motion of the skater is independent of the vertical motion, so we can ignore the vertical drop. By finding the time taken to travel the horizontal distance, we can determine the initial horizontal velocity. Using the equation x = vot and the equation for vertical motion, we can solve for the initial horizontal velocity.
Step-by-step explanation:
To calculate the skater's initial horizontal velocity, we can use the concept of projectile motion. The horizontal motion of the skater is independent of the vertical motion, which means we can ignore the vertical drop of 2.00 m. So, the horizontal length of the jump, which is 12.0 m, gives us the displacement in the horizontal direction.
Since the horizontal motion is at a constant velocity, the initial horizontal velocity is the same as the final horizontal velocity. Therefore, to find the initial horizontal velocity, we need to find the time taken to travel 12.0 m horizontally.
Using the equation x = vot, where x is the displacement, vo is the initial velocity, and t is the time, we can rearrange and solve for vo:
12.0 m = vot
Since the vertical drop does not affect the horizontal velocity, we can use the known acceleration due to gravity, g, to find the time, t. The vertical motion can be described using the equation h = vot + (1/2)gt2, where h is the vertical drop and g is the acceleration due to gravity.
Substituting the given values, we have:
2.00 m = (1/2)gt2
Solving for t, we find t = sqrt((2h)/g)
Substituting this value of t into the equation for the horizontal displacement, we can solve for vo as:
12.0 m = vo(sqrt((2h)/g))
Simplifying this equation gives us the initial horizontal velocity: vo = 12.0 m / sqrt((2h)/g)
Substituting the given values, we can calculate the initial horizontal velocity.