Final answer:
The initial horizontal velocity can be determined by separating the problem into vertical and horizontal components using projectile motion equations. Time of flight is calculated from the vertical drop, and horizontal velocity is then found using the horizontal distance traveled and the calculated time.
Step-by-step explanation:
The subject of the question is evaluating the initial horizontal velocity of a skateboarder who jumps off the top of a staircase and lands at the bottom given certain dimensions of a staircase. The solution involves applying the principles of kinematic equations related to projectile motion in the absence of air resistance, specifically focusing on the horizontal and vertical components separately as they are independent of each other.
For the vertical motion, we can use the equation for the displacement of an object under constant acceleration (in this case, gravity):
s represents the vertical displacement (2 m), u is the initial velocity (0 m/s since the skateboarder jumps horizontally), and a is the acceleration due to gravity (approximately 9.81 m/s2). t is the time taken to fall the vertical distance. Solving this for t gives us the time in the air.
For the horizontal motion, since there is no air resistance and no horizontal acceleration, the horizontal velocity is constant. Using the time t calculated from the vertical motion, the horizontal velocity v can be calculated using the equation
where d is the horizontal distance (12.0 m).
Following the above steps will provide the solution to the student's problem of finding the initial horizontal velocity.