.) Bailey has taken up parkour. She attempts to clear the gap between two buildings. Bailey is on a roof which is 50m high and she is attempting the jump to a building that is 42m high.
a.) If the two buildings were built touching (i.e. there is no gap) How long would it take for Bailey to drop down to the other building
b.) Now, since horizontal and vertical motions are completely independent, we can say that no matter how far the gap is, Haley MUST stay in the air for the length of time you found in part a.) If then she is running at 10m/s (about top speed for humans) and she goes off the roof perfectly horizontal, what is the max gap the two buildings may be separated by?
a) how long does free fall take to go 8 m?
b) find the time to cover the 8 meter gap;
time= 8/10 sec
now, how far did she fall in this time/
liska?
a.) To find the time it would take for Bailey to drop down from one building to another if there was no gap between them, we can use the laws of motion.
The vertical motion of Bailey can be described by the equation:
d = v₀t + (1/2)gt^2
Where:
d = vertical displacement (difference in height between the buildings)
v₀ = initial vertical velocity (0 m/s as Bailey starts from rest)
t = time taken
g = acceleration due to gravity (approximately 9.8 m/s²)
In this case, Bailey is dropping down, so the vertical displacement (d) will be negative. The initial vertical velocity (v₀) is 0 m/s. Let's assign a negative value to the displacement as Bailey's final position is lower than her initial position.
-8m = 0t + (1/2)(-9.8)t^2
Simplifying the equation, we can solve for t:
-4.9t^2 = -8
Dividing both sides by -4.9:
t^2 = 1.63
Taking the square root of both sides:
t ≈ 1.28 seconds
Therefore, it would take approximately 1.28 seconds for Bailey to drop down from one building to another if there was no gap between them.
b.) Since horizontal and vertical motions are completely independent, we can use the time found in part a to determine the maximum gap the two buildings may be separated by.
The horizontal displacement (x) can be calculated using the equation:
x = vt
Where:
x = horizontal displacement (gap between the buildings)
v = horizontal velocity (10 m/s, Bailey's running speed)
t = time taken (1.28 seconds)
Plugging in the values:
x = (10 m/s)(1.28 s)
x ≈ 12.8 meters
Therefore, the maximum gap the two buildings may be separated by is approximately 12.8 meters.