Janet jumps off a high diving platform with
a horizontal velocity of 2.25 m/s and lands in
the water 1.6 s later.
How high is the platform? The acceleration
of gravity is 9.8 m/s
2
h=gt²/2
12.54
To find the height of the platform, we can use the equations of motion. The vertical motion of the diver can be divided into two parts: the initial jump from the platform and the subsequent fall under the influence of gravity.
First, let's calculate the vertical distance traveled during the initial jump. We know that the horizontal velocity has no effect on the vertical motion, so we can ignore it for now.
The equation we can use to calculate the vertical distance is:
h = V₀t + (1/2)gt²
Where:
h = vertical distance (height)
V₀ = initial vertical velocity (0 m/s, as the diver starts from rest vertically)
t = time taken during the initial jump
g = acceleration due to gravity (9.8 m/s²)
In this case, the time taken during the initial jump is equal to the total time taken minus the time it takes to fall under the influence of gravity. So, the time taken during the initial jump is:
t = total time - time in free fall = 1.6 s - (2 × 0.8 s) = 1.6 s - 1.6 s = 0 s
Since the time taken during the initial jump is 0 seconds, the initial vertical velocity becomes irrelevant in this calculation.
Putting the values into the formula, we have:
h = 0 × 0 + (1/2) × 9.8 × 0²
h = 0 + 0
h = 0
Therefore, the height of the high diving platform is 0 meters.