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 3.0 s? express the speed in mi/h for a familiar comparison,
b) how far, in meters, does the object fall during the 3.0 s? How many floors does the dormitory probably have?
come on now, use what we have done
v = g t
but to go from m/s to mi/hr
use
3600 seconds / hour
and 1609 meters/mile
a floor is about 3 meters
WORK IN METRIC
convert later if dealing with carpenters.
is it d = 1/2 (9.8) (3)^2 = 44.1 m/s^2/3s =14.7 m/s x 2 = 32.87 = 32.87 mi/h?
and
b) d= 1/2 (9.8) (3)^2 =44.1 m/s^2/35 = 14.7 m/s
You are terrribly fouled up with units. Give me a minute
the ground is 3 seconds down
d = (1/2) (9.81) (3)^2 correct
d = 44.1 METERS (THAT IS PART B)
(that is 9.81 m/s^2 * 9 s^2 so just m or meters)
NOW THE SPEED (Part A)
v = g t
v = 9.81 m/s^2 * 3 s = 29.4 m/s
(THAT IS PART A)
BUT they want miles/ hr
so
29.4 m/s * 1 mile/1609 m * 3600 s/h
= 65.8 miles/hour
To answer these questions, we need to consider the equations of motion under constant acceleration. In this case, since we are neglecting air resistance, we can assume the acceleration due to gravity remains constant at approximately 9.8 m/s².
a) To find the speed of the object when it strikes the ground after 3.0 seconds, we can use the equation for displacement under constant acceleration:
vf = vi + at
Where:
vf = final velocity,
vi = initial velocity (which is zero in this case),
a = acceleration (in this case, acceleration due to gravity),
t = time.
Let's calculate it step by step:
1. First, let's calculate the final velocity (vf) at 3.0 seconds:
vf = 0 + (9.8 m/s²) * 3.0 s
= 29.4 m/s
2. Next, we can convert the velocity from meters per second (m/s) to miles per hour (mi/h):
vf_mph = vf * (2.23694 mi/h) [1 meter = 2.23694 miles]
vf_mph = 29.4 * 2.23694
= 65.66 mi/h
Therefore, the object is traveling at approximately 65.66 mi/h when it strikes the ground.
b) To find the distance the object falls during the 3.0 seconds, we can use the equation for displacement:
d = vi * t + (1/2) * a * t²
Where:
d = distance,
vi = initial velocity,
t = time,
a = acceleration.
Let's calculate it step by step:
1. Since the initial velocity (vi) is zero, the equation simplifies to:
d = (1/2) * a * t²
2. Plugging in the values:
d = (1/2) * (9.8 m/s²) * (3.0 s)²
≈ 44.1 m
Therefore, the object falls approximately 44.1 meters during the 3.0 seconds.
To estimate the number of floors in the dormitory, we need to make an assumption about the height of each floor. Let's assume each floor is approximately 3 meters high (which is a common estimate). We can then divide the distance fallen (44.1 meters) by the height of each floor (3 meters) to find the number of floors:
Number of floors = d / height of each floor
= 44.1 m / 3 m
≈ 14.7 floors
Since the number of floors can't be fractional, we can assume that the dormitory probably has approximately 15 floors.
Note: These calculations assume no air resistance and a constant acceleration due to gravity, which may not be entirely accurate in practice.