Final answer:
Using kinematic equations, the original speed of the quarter is calculated based on the time taken to reach the peak of its motion (1.25 seconds). Accounting for the acceleration due to gravity, the initial velocity comes out to 12.25 m/s, which is option A.
Step-by-step explanation:
The question concerns the physics of projectile motion. To find the quarter’s original speed when it is flipped and returns to the point from which it was flipped after 2.5 seconds with an acceleration of 9.8 m/s² downward, we can use the kinematic equations for uniformly accelerated motion.
The total time for the quarter to travel upward and then return down is 2.5 seconds, which means it takes 1.25 seconds to reach the peak of its trajectory (half of the total time, since the upward and downward journeys are symmetrical). At the peak, the velocity of the quarter is 0 m/s due to gravity. Therefore, the initial velocity can be found by using the equation v = u + at, where:
- v is the final velocity (0 m/s at the peak)
- u is the initial velocity
- a is the acceleration (negative here, as it is downward)
- t is the time (1.25 s to the peak)
By rearranging the equation to solve for u, we get u = v - at, which means:
u = 0 - (-9.8 m/s² * 1.25 s) = 12.25 m/s. Therefore, the quarter's original speed is 12.25 m/s, which corresponds to option A