Math

QuestionCalculate the depth of a well if a bucket falls for 9.3 seconds. Round to the nearest tenth. Use d=12gt2d = \frac{1}{2}gt^2.

Studdy Solution

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 0m/s0\, m/s.
4. The time of fall is 9.3seconds9.3\, seconds.

STEP 2

We can use the equation of motion to find the depth of the well. The equation of motion is given byd=vit+0.5at2d = v_i t +0.5 a t^2where- dd is the distance (depth of the well), - viv_i is the initial velocity, - aa is the acceleration (due to gravity), and- tt is the time.

STEP 3

Now, plug in the given values for the initial velocity, acceleration, and time into the equation of motion.
d=09.3+0.59.8(9.3)2d =0 \cdot9.3 +0.5 \cdot9.8 \cdot (9.3)^2

STEP 4

Calculate the depth of the well.
d=0.9.8(9.3)2=424.435md =0. \cdot9.8 \cdot (9.3)^2 =424.435\, m

STEP 5

Round the depth of the well to the nearest tenth.
d424.4md \approx424.4\, mThe depth of the well is approximately424.4 meters.

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