Math Snap

STEP 1

Assumptions1. The bucket falls freely, meaning it is only affected by gravity and not by any other forces (like air resistance).
. The acceleration due to gravity is approximately 9.8\, m/s^.
3. The bucket starts from rest, meaning its initial velocity is $0\, m/s$.
4. The time of fall is $9.3\, seconds$.

STEP 2

We can use the equation of motion to find the depth of the well. The equation of motion is given by$$d = v_i t +0.5 a t^2$$where- $d$ is the distance (depth of the well),
- $v_i$ is the initial velocity,
- $a$ is the acceleration (due to gravity), and- $t$ is the time.

STEP 3

Now, plug in the given values for the initial velocity, acceleration, and time into the equation of motion.
$$d =0 \cdot9.3 +0.5 \cdot9.8 \cdot (9.3)^2$$

STEP 4

Calculate the depth of the well.
$$d =0. \cdot9.8 \cdot (9.3)^2 =424.435\, m$$

Round the depth of the well to the nearest tenth.
$$d \approx424.4\, m$$The depth of the well is approximately424.4 meters.