To calculate the velocity at which a stone will strike the ground when dropped from the top of a building or thrown vertically downward, we can use the equations of motion under constant acceleration due to gravity.
- Stone dropped from the top of a building: When the stone is dropped, it falls freely under the influence of gravity. The acceleration due to gravity is approximately 32.2 ft/s² (or 9.8 m/s²).
To find the final velocity when it strikes the ground, we can use the equation: v² = u² + 2as
where: v = final velocity (unknown) u = initial velocity (which is 0 in this case since the stone is dropped) a = acceleration due to gravity (-32.2 ft/s²) s = displacement (400 ft, as the stone is dropped from a height of 400 ft)
Plugging in the values, the equation becomes: v² = 0² + 2 * (-32.2) * 400
Simplifying: v² = -25680
Taking the square root of both sides (ignoring the negative sign as velocity is a scalar quantity): v ≈ 160 ft/s
Therefore, when the stone is dropped from the top of the building, it will strike the ground with a velocity of approximately 160 ft/s.
- Stone thrown vertically downward with an initial velocity: In this case, the stone is thrown downward with an initial velocity of 36 ft/s. The acceleration due to gravity remains the same at approximately 32.2 ft/s².
Using the same equation as before: v² = u² + 2as
Substituting the given values: v² = 36² + 2 * (-32.2) * 400
Simplifying: v² = 1296 - 25760
v² = -24464
Taking the square root (ignoring the negative sign): v ≈ 156.4 ft/s
Therefore, when the stone is thrown vertically downward with an initial velocity of 36 ft/s, it will strike the ground with a velocity of approximately 156.4 ft/s.