Final answer:
To determine the landing point of the plate flying off the countertop, we calculate the time of flight using the vertical distance and gravity, then multiply by the horizontal velocity. This physics problem is a classic example of projectile motion.
Step-by-step explanation:
To solve the problem of how far from the end of the countertop a sliding plate will land, we need to apply principles from projectile motion in physics. The horizontal velocity of the plate as it leaves the countertop is constant because there is no acceleration in the horizontal direction (assuming air resistance is negligible). Therefore, the only acceleration is due to gravity, which acts in the vertical direction. The first step is to determine the time it takes for the plate to hit the floor. Since the countertop is 4.05 meters above the floor and the plate falls due to gravity, we can use the following kinematic equation for vertical motion:
t = sqrt(2h/g), where h is the height (4.05m) and g is the acceleration due to gravity (9.8m/s2).
Next, we find the horizontal distance travelled using the horizontal velocity and the time of flight:
distance = velocity × time, where the velocity is 0.54 m/s (the speed it was slid at) and time is what we calculated from the vertical motion. By performing these calculations, we can find out where the plate will land relative to the base of the countertop.