a projectile is dropped from the top of a building - it falls 1900 ft prior to reaching the ground. determine the magnitude of the acceleration in ft/second squared to the nearest tenth.
Question 1 options:
To determine the magnitude of the acceleration of the projectile, we can use the kinematic equation for motion under constant acceleration:
d = (1/2) * a * t^2
Where:
d is the displacement (1900 ft)
a is the acceleration (what we're trying to find)
t is the time it takes for the projectile to fall
Since the projectile is dropped (not thrown), its initial velocity is 0 ft/s. For an object in free fall near the surface of the Earth, the acceleration due to gravity is approximately 32.2 ft/s^2.
We can rearrange the equation to solve for the acceleration:
a = (2 * d) / t^2
Since the time t is not given in the question, we need to find it. The time it takes for the projectile to fall can be calculated using the equation:
d = (1/2) * g * t^2,
where g is the acceleration due to gravity. Rearranging the equation, we have:
t = sqrt((2 * d) / g)
Substituting the given values into the equation, we get:
t ≈ sqrt((2 * 1900 ft) / (32.2 ft/s^2)) ≈ 8.04 s (rounded to two decimal places)
Now, we can substitute the value of t back into the formula for acceleration:
a = (2 * 1900 ft) / (8.04 s)^2 ≈ 59.6 ft/s^2 to the nearest tenth.
Therefore, the magnitude of the acceleration of the projectile is approximately 59.6 ft/s^2 (to the nearest tenth).