Final answer:
The skateboarder will take approximately 9.83 seconds to reach the bottom 120m away.
Step-by-step explanation:
To calculate the time it takes for the skateboarder to reach the bottom 120m away, we can use the kinematic equation: d = v0t + 1/2at2. In this equation, d represents the distance, v0 represents the initial velocity, a represents the acceleration, and t represents the time. Knowing that the initial velocity v0 = 3.5m/s, the acceleration a = 1.5m/s², and the distance d = 120m, we can rearrange the equation to solve for t: 120m = (3.5m/s)t + (1/2)(1.5m/s²)(t2). This equation can be simplified to a quadratic equation, which can be solved to determine the value of t.
The quadratic equation is 0.75t2 + 3.5t - 120 = 0. By using the quadratic formula t = (-b ± √(b2 - 4ac)) / (2a), where a = 0.75, b = 3.5, and c = -120, we can calculate the values of t by substituting these values into the formula. Discarding the negative value, we find that t ≈ 9.83 seconds.