Final answer:
To determine how tall the person is upon whose head the marshmallow landed, we use the free-fall formula h = ½gt² using the known height and time, calculating the distance fallen by the marshmallow, and subtracting that from the initial height to find the height of the person's head as approximately 1.62 meters.
Step-by-step explanation:
To solve the challenge question where a marshmallow is dropped from a 5-meter high pedestrian bridge and lands 0.83 seconds later on a person's head, we first need to know the equation of motion to calculate the height at which the marshmallow hit the unsuspecting person's head.
- What do you know? The initial height (h) from which the marshmallow is dropped is 5 meters, and the time (t) it takes to hit the person is 0.83 seconds.
- What do you need to solve for? The height of the person with the marshmallow on their head.
- What equation(s) will you use? The equation to use is the free-fall formula h = ½gt², where h is the height the object falls from, g is the acceleration due to gravity (typically 9.8 m/s²), and t is the time.
- What is the solution to this problem? Plugging the known values into the formula:
h = ½gt²
= 0.5 × 9.8 × (0.83)²
= 0.5 × 9.8 × 0.6889
= 3.3777 meters
As the marshmallow was initially dropped from 5 meters, the height at which the marshmallow hit the person's head is 5 meters - 3.3777 meters = 1.6223 meters. Therefore, the person's height is approximately 1.62 meters.