Final answer:
For a coin thrown upward with a velocity of 12.4 m/s, it will remain in the air for a total of 2.53 seconds and reach a maximum height of 7.84 meters using the principles of physics and projectile motion.
Step-by-step explanation:
The question pertains to the physics of a coin being thrown upward with a certain initial velocity. To determine how long the coin will remain in the air and how high it will rise, we can use the kinematic equations for projectile motion.
(a) To find the total time the coin stays in the air, we first calculate the time it takes to reach its highest point, where its velocity will be zero:
t = v / g = 12.4 m/s / 9.8 m/s² = 1.265 s
The total time in the air will be twice this value, as the descent takes the same amount of time:
Total time = 2 * 1.265 s = 2.53 s
(b) To find the maximum height the coin will reach, use the equation:
h = (v²) / (2 * g) = (12.4 m/s)² / (2 * 9.8 m/s²) = 7.84 m