To determine the horizontal speed required for Elana to safely land in the pool, follow these steps:
1. Calculate the time of flight (t) using the equation for vertical motion:
- h = (1/2)gt^2
Given that h = 25.0 m and g = 9.8 m/s^2:
- t = sqrt((2 * 25.0 m) / (9.8 m/s^2))
- t ≈ 2.26 s
2. Use the time of flight to find the horizontal speed (vx) needed for Elana to travel 14.3 m:
- d = vx * t
Given that d = 14.3 m:
- vx = 14.3 m / 2.26 s
- vx ≈ 6.34 m/s
Therefore, Elana must be running at a horizontal speed of approximately 6.34 m/s when she leaves the building to safely land in the pool.