MUHAMMAD SHAKIR A. answered • 04/19/23
Online Physics tutor
When you drop a stone from rest, its initial velocity is zero. Therefore, we can use the kinematic equation for free fall to calculate the distance it falls vertically in the first 9 seconds:
h = 1/2 * g * t^2
where h is the distance fallen, g is the acceleration due to gravity, and t is the time.
Plugging in the values given, we get:
h = 1/2 * 9.8 m/s^2 * (9 s)^2 = 441 m
Therefore, the stone falls vertically 441 meters in the first 9 seconds when dropped from rest.
When you toss the stone horizontally at 3.7 m/s, it still falls vertically due to the force of gravity acting on it. However, its horizontal velocity will cause it to travel a distance in the horizontal direction as it falls.
To calculate the distance it falls vertically, we can use the same equation as before. However, the time it takes to fall will be slightly longer than 9 seconds because it will also be moving horizontally. The horizontal distance it travels can be calculated using the equation:
d = v_x * t
where d is the distance traveled horizontally, v_x is the horizontal velocity, and t is the time.
Since the stone is moving horizontally at a constant velocity, its horizontal distance traveled will be:
d = v_x * t = 3.7 m/s * 9 s = 33.3 m
Now, we can use the vertical distance equation to calculate how far the stone falls in the first 9 seconds. The time it takes to fall vertically will be slightly longer than 9 seconds because it is also moving horizontally, but we can use the total time it takes to hit the ground:
h = 1/2 * g * t^2
where t is the time it takes for the stone to hit the ground. To find this time, we can use the horizontal distance and the horizontal velocity:
t = d / v_x = 33.3 m / 3.7 m/s = 9 seconds (rounded)
Plugging in the values, we get:
h = 1/2 * 9.8 m/s^2 * (9 s)^2 = 441 m
Therefore, the stone falls vertically 441 meters in the first 9 seconds when tossed horizontally at 3.7 m/s.
