Final answer:
Miguel would take approximately 5.75 seconds to reach the ground if he falls freely from an altitude of 162 meters with an acceleration due to gravity of 9.8 m/s².
Step-by-step explanation:
To calculate the time it takes for Miguel to reach the ground from an altitude of 162 meters while in free fall, we can use the kinematic equation for uniformly accelerated motion, which is d = ½ at², where ‘d’ is the distance, ‘a’ is the acceleration due to gravity (9.8 m/s²), and ‘t’ is the time in seconds. Rearranging the formula to solve for time (‘t’), we get t = √(2d/a). Plugging in the values for ‘d’ (162 meters) and ‘a’ (9.8 m/s²), we can calculate the time taken for Miguel to hit the ground.
By calculating, t = √(2*162/9.8) = √(324/9.8) = √(33.06) ≈ 5.75 seconds.
Therefore, it would take Miguel approximately 5.75 seconds to reach the ground if he falls freely from an altitude of 162 meters.