Stone dropped from 78.4m height - find time and velocity
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We have a free fall motion problem. A stone is dropped from a height of 78.4 meters. The stone starts with zero initial velocity and falls under the influence of gravity, which is 9.8 meters per second squared. We need to find the time taken to reach the ground and the final velocity.
To find the time of fall, we use the kinematic equation s equals u t plus half g t squared. Since the stone is dropped, the initial velocity u is zero. Substituting our values: 78.4 equals half times 9.8 times t squared. This simplifies to 78.4 equals 4.9 t squared. Solving for t squared gives us 16, so t equals 4 seconds.
Now we find the final velocity using v equals u plus g t. Substituting our values: v equals zero plus 9.8 times 4, which gives us 39.2 meters per second. We can verify this using the alternative equation v squared equals u squared plus 2 g s. This gives v squared equals 1536.64, so v equals 39.2 meters per second, confirming our answer.
Now let's watch the stone fall in real time. As time progresses from 0 to 4 seconds, we can see how the stone's position changes, its velocity increases linearly with time, and the height decreases according to our kinematic equation. Notice how the velocity arrow grows longer as the stone accelerates downward.
In conclusion, we have solved the free fall problem completely. The stone dropped from a height of 78.4 meters takes exactly 4 seconds to reach the ground and strikes the ground with a velocity of 39.2 meters per second. These results were obtained using fundamental kinematic equations for uniformly accelerated motion under gravity.