Answer:
14 m/s
Explanation:
The child is falling due to constant gravitational acceleration.
This means we can use a kinematics equation to relate:
First, we can list our knowns (givens):
- distance = Δx = 10 m
- mass = m = 40 kg
- initial velocity = vᵢ = 0 m/s
- gravitational acceleration = g = 9.8 m/s²
We are solving for:
This means we can use the combined kinematics equation to relate the knowns and unknowns:
- \(v_f^2 = v_i^2 + 2a\Delta x\)
where:
- \(v_f\) = final velocity
- \(v_i\) = initial velocity
- \(a\) = acceleration
- \(\Delta x\) = change in position (distance traveled)
Plugging in the known values, we get:
\(v_f^2 = (0\text{ m/s})^2 + 2\!\left(9.8\text{ m/s}^2\right)\!(10\text{ m})\)
Solving for \(v_f\), we get:
\(v_f^2 = 196\text{ m}^2/\text{s}^2\)
\(v_f = \sqrt{196\text{ m}^2/\text{s}^2}\)
\(\boxed{v_f = 14\text{ m/s}}\)
So, the child is moving 14 meters per second right before he hits the water.
