Final answer:
To find the distance the penguin lands from the iceberg, we calculate the fall time using the vertical distance (4.50 m) and the acceleration due to gravity. Multiplying the horizontal velocity (6.30 m/s) by the fall time we obtained (0.958 s), we get the horizontal landing distance, which is approximately 6.03 m.
Step-by-step explanation:
The question involves calculating the horizontal distance a penguin lands from the edge of an iceberg after sliding off with a given horizontal velocity. This is a problem related to projectile motion in physics, specifically the horizontal motion component.
To calculate the distance the penguin lands from the iceberg, we use the formula for the time of fall, which only depends on the vertical motion.
The time (t) it takes an object to fall a certain vertical distance (d) with no initial vertical velocity and under constant acceleration due to gravity (g) is given by the equation d = ½ gt^2. This can be rearranged to solve for t. With the given distance of 4.50 m, and g = 9.81 m/s^2:
t = √(2d/g) = √(2*4.50 m / 9.81 m/s^2) = √(0.917 s^2) = 0.958 s (rounded to three significant figures)
Since there is no acceleration in the horizontal direction, the horizontal distance (x) the penguin travels before hitting the water is the product of its initial horizontal velocity (vx) and the time of fall:
x = vx * t = 6.30 m/s * 0.958 s = 6.03 m
This distance does not match any of the multiple-choice options provided, indicating there may have been a mistake in the question or in the available answers. The penguin will land approximately 6.03 m from the edge of the iceberg if it slides off horizontally with a velocity of 6.30 m/s and the water is 4.50 m below.