A student drops an object out the window of the top floor of a high-rise dormitory.
(a)Neglecting air resistance, how fast is the object traveling when it strikes the ground at the end of 2.9 s? Express the speed in mi/h for a familiar comparison.
Can things dropped from high places be dangerous to people below? (Assume that a falling object can be dangerous if its speed exceeds 35 mi/h.)
(b)How far, in meters, does the object fall during the 2.9 s?
How many floors does the dormitory have?. (Assume 4 m/floor.)
(a) To calculate the speed of the object when it strikes the ground, we can use the equation for free fall motion:
v = gt,
where v is the final velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
First, let's convert 2.9 seconds to hours:
2.9 s * (1 hr / 3600 s) = 0.0008056 hr
Now we can calculate the speed in mi/h:
v = (9.8 m/s^2) * (0.0008056 hr) * (1 km / 1000 m) * (0.6214 mi / 1 km) * (1 hr / 1 h)
v ≈ 0.0003732 mi/h
So the speed of the object when it strikes the ground is approximately 0.0003732 mi/h, which is negligible.
Yes, things dropped from high places can be dangerous to people below if their speed exceeds 35 mi/h. In this case, the speed is much lower than that, so it should not be a concern.
(b) The distance, in meters, that the object falls during the 2.9 s can be calculated using the equation:
d = (1/2) * g * t^2,
where d is the distance, g is the acceleration due to gravity, and t is the time.
d = (1/2) * (9.8 m/s^2) * (2.9 s)^2
d ≈ 40.046 m
So the object falls approximately 40.046 meters during the 2.9 s.
(c) To determine how many floors the dormitory has, we can divide the distance fallen by the height of each floor:
Number of floors = distance fallen / height of each floor
Number of floors = 40.046 m / 4 m/floor
Number of floors ≈ 10.011
Since we can't have a fraction of a floor, we round down to the nearest whole number.
So the dormitory has approximately 10 floors.
(a) v = gt, so v(2.9) = 9.81 * 2.9 = ____ m/s
35 mi/hr * 1609m/mi * 1hr/3600s = (35*1609)/3600 = ____ m/s
(b) s = 1/2 gt^2
floors = (b)/4