The time needed for the hammer to reach the surface of the Earth is 3.54 s.
<h3>
Time of motion of the hammer</h3>
The time of motion is calculated as follows;
t = √(2h/g)
where;
- h is height of fall
- g is acceleration due to gravity
t = √(2 x 10 / 1.6)
t = 3.54 s
Thus, the time needed for the hammer to reach the surface of the Earth is 3.54 s.
Learn more about time of motion here: brainly.com/question/2364404
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B. velocity at position x, velocity at position x=0, position x, and the original position
In the equation
=
+2 a x (x - x₀)
= velocity at position "x"
= velocity at position "x = 0 "
x = final position
= initial position of the object at the start of the motion
Answer:
a) ![h=250\ m](https://tex.z-dn.net/?f=h%3D250%5C%20m)
b) ![\Delta h=0.0835\ m](https://tex.z-dn.net/?f=%5CDelta%20h%3D0.0835%5C%20m)
Explanation:
Given:
- upward acceleration of the helicopter,
![a=5\ m.s^{-2}](https://tex.z-dn.net/?f=a%3D5%5C%20m.s%5E%7B-2%7D)
- time after the takeoff after which the engine is shut off,
![t_a=10\ s](https://tex.z-dn.net/?f=t_a%3D10%5C%20s)
a)
<u>Maximum height reached by the helicopter:</u>
using the equation of motion,
![h=u.t+\frac{1}{2} a.t^2](https://tex.z-dn.net/?f=h%3Du.t%2B%5Cfrac%7B1%7D%7B2%7D%20a.t%5E2)
where:
u = initial velocity of the helicopter = 0 (took-off from ground)
t = time of observation
![h=0+0.5\times 5\times 10^2](https://tex.z-dn.net/?f=h%3D0%2B0.5%5Ctimes%205%5Ctimes%2010%5E2)
![h=250\ m](https://tex.z-dn.net/?f=h%3D250%5C%20m)
b)
- time after which Austin Powers deploys parachute(time of free fall),
![t_f=7\ s](https://tex.z-dn.net/?f=t_f%3D7%5C%20s)
- acceleration after deploying the parachute,
![a_p=2\ m.s^{-2}](https://tex.z-dn.net/?f=a_p%3D2%5C%20m.s%5E%7B-2%7D)
<u>height fallen freely by Austin:</u>
![h_f=u.t_f+\frac{1}{2} g.t_f^2](https://tex.z-dn.net/?f=h_f%3Du.t_f%2B%5Cfrac%7B1%7D%7B2%7D%20g.t_f%5E2)
where:
initial velocity of fall at the top = 0 (begins from the max height where the system is momentarily at rest)
time of free fall
![h_f=0+0.5\times 9.8\times 7^2](https://tex.z-dn.net/?f=h_f%3D0%2B0.5%5Ctimes%209.8%5Ctimes%207%5E2)
![h_f=240.1\ m](https://tex.z-dn.net/?f=h_f%3D240.1%5C%20m)
<u>Velocity just before opening the parachute:</u>
![v_f=u+g.t_f](https://tex.z-dn.net/?f=v_f%3Du%2Bg.t_f)
![v_f=0+9.8\times 7](https://tex.z-dn.net/?f=v_f%3D0%2B9.8%5Ctimes%207)
![v_f=68.6\ m.s^{-1}](https://tex.z-dn.net/?f=v_f%3D68.6%5C%20m.s%5E%7B-1%7D)
<u>Time taken by the helicopter to fall:</u>
![h=u.t_h+\frac{1}{2} g.t_h^2](https://tex.z-dn.net/?f=h%3Du.t_h%2B%5Cfrac%7B1%7D%7B2%7D%20g.t_h%5E2)
where:
initial velocity of the helicopter just before it begins falling freely = 0
time taken by the helicopter to fall on ground
height from where it falls = 250 m
now,
![250=0+0.5\times 9.8\times t_h^2](https://tex.z-dn.net/?f=250%3D0%2B0.5%5Ctimes%209.8%5Ctimes%20t_h%5E2)
![t_h=7.1429\ s](https://tex.z-dn.net/?f=t_h%3D7.1429%5C%20s)
From the above time 7 seconds are taken for free fall and the remaining time to fall with parachute.
<u>remaining time,</u>
![t'=t_h-t_f](https://tex.z-dn.net/?f=t%27%3Dt_h-t_f)
![t'=7.1428-7](https://tex.z-dn.net/?f=t%27%3D7.1428-7)
![t'=0.1428\ s](https://tex.z-dn.net/?f=t%27%3D0.1428%5C%20s)
<u>Now the height fallen in the remaining time using parachute:</u>
![h'=v_f.t'+\frac{1}{2} a_p.t'^2](https://tex.z-dn.net/?f=h%27%3Dv_f.t%27%2B%5Cfrac%7B1%7D%7B2%7D%20a_p.t%27%5E2)
![h'=68.6\times 0.1428+0.5\times 2\times 0.1428^2](https://tex.z-dn.net/?f=h%27%3D68.6%5Ctimes%200.1428%2B0.5%5Ctimes%202%5Ctimes%200.1428%5E2)
![h'=9.8165\ m](https://tex.z-dn.net/?f=h%27%3D9.8165%5C%20m)
<u>Now the height of Austin above the ground when the helicopter crashed on the ground:</u>
![\Delta h=h-(h_f+h')](https://tex.z-dn.net/?f=%5CDelta%20h%3Dh-%28h_f%2Bh%27%29)
![\Delta h=250-(240.1+9.8165)](https://tex.z-dn.net/?f=%5CDelta%20h%3D250-%28240.1%2B9.8165%29)
![\Delta h=0.0835\ m](https://tex.z-dn.net/?f=%5CDelta%20h%3D0.0835%5C%20m)
Answer:
Systematic errors.
Explanation:
The density of the aluminium was calculated by a human and this is not natural but can be due to errors in the calibration of the scale for measuring the weight or taking readings from the measuring cylinder.
Random errors are natural errors. Random errors in experimental measurements are caused by unknown and unpredictable changes in the experiment. Systematic errors are due to imprecision or problems with instruments.