Respuesta :
Answer:
19.62 m
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
[tex]\frac{s}{4}=ut+\frac{1}{2}at^2\\\Rightarrow \frac{s}{4}=0t+\frac{1}{2}\times a\times t^2\\\Rightarrow \frac{s}{4}=\frac{1}{2}at^2[/tex]
[tex]\frac{3}{4}s=ut+\frac{1}{2}at^2\\\Rightarrow \frac{3}{4}s=u1+\frac{1}{2}\times a\times 1^2\\\Rightarrow \frac{s}{4}=\frac{u}{3}+\frac{1}{6}a[/tex]
Now the initial velocity of the last half height will be the final velocity of the first half height.
[tex]v=u+at\\\Rightarrow v=at[/tex]
Since the height are equal
[tex]\frac{1}{2}at^2=\frac{u}{3}+\frac{1}{6}a\\\Rightarrow \frac{1}{2}at^2=\frac{at}{3}+\frac{1}{6}a\\\Rightarrow 3t^2-2t-1=0[/tex]
[tex]t=\frac{-\left(-2\right)+\sqrt{\left(-2\right)^2-4\cdot \:3\left(-1\right)}}{2\cdot \:3}, t=\frac{-\left(-2\right)-\sqrt{\left(-2\right)^2-4\cdot \:3\left(-1\right)}}{2\cdot \:3}\\\Rightarrow t=1, -\frac{1}{3}[/tex]
Time taken to first 25% of the fall is 1 second
Total time taken = 2 seconds
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow s=0\times t+\frac{1}{2}\times 9.81\times 2^2\\\Rightarrow s=19.62\ m[/tex]
The height from which the object was dropped was 19.62 m
By using the motion equations, we will see that the object is dropped from a height of 8.71 meters.
Finding the motion equations.
We should start with the acceleration, which will be equal to the gravitational acceleration, then we have:
a(t) = -9.8 m/s^2
To get the velocity equation we integrate over time, because the object is dropped, it does not have initial velocity, thus there is no constant of integration.
v(t) = (-9.8 m/s^2)*t
To get the position we integrate again, here the constant of integration is the initial height, then we have:
p(t) = (-4.9 m/s^2)*t^2 + H
The time in which the object falls to the ground is given by:
p(t) = 0 = (-4.9 m/s^2)*t^2 + H
(4.9 m/s^2)*t^2 = H
t = √(H/4.9 m/s^2)
And we know that 75% of that is equal to 1s, then:
0.75*√(H/4.9 m/s^2) = 1s
Now we can solve this for H.
H = (4.9m/s^2)(1s/0.75)^2 = 8.71m
So the object is dropped from 8.71 meters.
If you want to learn more about motion equations, you can read:
https://brainly.com/question/11049671
