An object falls from height h from rest and travels 0.45h in the last 1.00 s.
(a) Find the time of its fall.
(b) Find the height of its fall.
I've tried multiple times but I cannot get the correct answer.
I assume that is .45m in the last second.
WEll, its average veloicty was .45m/s. Knowing its acceleration,
vf=vi+at in the last second, but avg velocity= vf+vi)/2 or
2 avgvel=vf+ vi or vi=2avgv-vf
vf=2avgv-vf+g
2vf=2avgv+g
vf=avgv + g/2 so solve for vf
Finally,
v=gtimefall solve for time of fall
h=1/2 g t^2
bobpursley,
No, the question actually says it travels 0.45h in the last second. So its 45% of the total height I believe. Unless it was a typo the average velocity is unknown. The only information known is its initial velocity (at the top of the fall, not only the last second) and the distance (0.45h) it falls in the last second.
To solve this problem, we can use the equations of motion for free-falling objects. We can start by breaking down the given information:
1. The object falls from a height h.
2. It travels a distance of 0.45h in the last 1.00 second.
(a) To find the time of its fall, we can use the equation:
d = ut + (1/2)at²
where:
- d is the distance traveled (0.45h)
- u is the initial velocity (0 m/s as the object starts from rest)
- t is the time of fall (unknown)
- a is the acceleration due to gravity (-9.8 m/s²)
Substituting the values into the equation, we have:
0.45h = 0 + (1/2)(-9.8)(1.00)²
Calculating this equation, we get:
0.45h = -4.9
To isolate h, we divide both sides of the equation by 0.45:
h = -4.9 / 0.45
This will give us the height of the fall.
(b) To find the height of its fall, we can use the equation:
s = ut + (1/2)at²
where:
- s is the final displacement (0.45h)
- u is the initial velocity (0 m/s)
- t is the time of fall (unknown)
- a is the acceleration due to gravity (-9.8 m/s²)
Substituting the values into the equation, we have:
0.45h = 0(1.00) + (1/2)(-9.8)(t)²
Simplifying the equation, we get:
0.45h = -4.9t²
To calculate the time of fall, we need to re-arrange the equation:
t² = -0.45h / 4.9
Taking the square root of both sides, we have:
t = √(-0.45h / 4.9)
Now, we have obtained an expression for the time of fall. We can substitute this value back into the equation we got for part (a) to find the height of the fall.