Final answer:
To calculate how far from the base of the diving board you would land, you use the concepts of projectile motion, calculating the time in the air based on the height of the dive and the gravitational acceleration, and then calculate the range using the initial horizontal velocity and the time of flight.
Therefore, you would land approximately 2.65 meters (or about 8.7 feet) from the base of the diving board.
Step-by-step explanation:
To determine how far from the base of the diving board you land after jumping horizontally at 5.0 ft/s from a height of 15 ft, you need to consider the physics of projectile motion. In projectile motion, the horizontal (x) and vertical (y) components of the motion are independent. The horizontal distance covered, also known as range, depends on the initial horizontal velocity and the time in the air.
The time in the air can be calculated using the vertical component of the motion, assuming constant acceleration due to gravity, which is -9.8 m/s2 (or about -32.2 ft/s2 when using feet). Since you're starting with an initial vertical velocity of 0 (since you're jumping out horizontally), you can use the following equation to find the time (t) the jumper is in the air:
t = sqrt(2 * height / g)
Substituting the given values and converting feet to meters for consistency (1 ft = 0.3048 m):
t = sqrt(2 * 15 ft * 0.3048 m/ft / 9.8 m/s2)
t ≈ 1.74 s
Now, to find the horizontal distance traveled (range), use:
Range = initial velocity * time
Converting the velocity to meters per second:
5.0 ft/s * 0.3048 m/ft = 1.524 m/s
Range = 1.524 m/s * 1.74 s
Range ≈ 2.65 m
Therefore, you would land approximately 2.65 meters (or about 8.7 feet) from the base of the diving board.