Final answer:
The marble, involved in projectile motion, will take approximately 0.73 seconds to hit the ground when launched horizontally off a table, using the vertical motion formula. However, this correct answer is not listed among the given options.
Step-by-step explanation:
The question concerns the time it takes for a marble to hit the ground after being launched horizontally off a table. This problem is categorized under projectile motion in physics. To find the time, we use the formula for the vertical motion of the marble, given by
d = ½ gt^2
where:
- d is the vertical distance the marble falls (2.62 meters)
- g is the acceleration due to gravity (9.81 m/s²)
- t is the time in seconds.
Thus, we solve for t:
2.62 = ½ * 9.81 * t^2
5.24 = 9.81 * t^2
t^2 = 5.24 / 9.81
t^2 = 0.534
t = √0.534
t ≈ 0.73 seconds
Since 0.73 seconds is not one of the given options, we can see that there's a discrepancy which might be due to either using the wrong value for the distance, a typo in the options, or an incorrect interpretation of the given data. Hence, none of the options (a) 0.26 seconds, (b) 0.50 seconds, (c) 1.00 seconds, or (d) 2.00 seconds is correct based on our calculation.