# A steel ball of mass 4-kg is dropped from rest

Donald Johnson 2021-12-29 Answered
A steel ball of mass 4-kg is dropped from rest from the top of a building. If the air resistance is 0.012v and the ball hits the ground after 2.1 seconds, how tall is the building? Answer in four decimal places.
You can still ask an expert for help

## Want to know more about Laplace transform?

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Piosellisf
Mass of the ball $m=4kg$
Dropped from nest do initial velocity is zero is
Given that air resistence $=0.012v$
The equation of motion is
$m\frac{dv}{dt}=g-0.012v$
or $\frac{dv}{dt}=\frac{g-0.012v}{m}$
$=\frac{g-0.012v}{4}$
$\frac{dv}{g-0.012v}=\frac{dt}{4}$
or $\frac{d\left(g-0.012v\right)}{-0.012\left(g-0.012v\right)}=\frac{dt}{4}$
or $\frac{d\left(g-0.012v\right)}{g-0.012v}=\frac{dt}{4}$
$=-0.003dt$
Integrating $\int \frac{d\left(g-0.012v\right)}{g-0.012v}=-0.003\int dt+c$
or $\mathrm{ln}\left(g-0.012v\right)=-0.003t+C$
Initially
$\therefore PSK\mathrm{ln}\left(g\right)=c$
$\therefore \mathrm{ln}\left(g-0.012v\right)=-0.003t+\mathrm{ln}g$
$\mathrm{ln}\left(\frac{g-0.012v}{g}\right)=-0.003t$
$\frac{g-0.012v}{g}={e}^{-0.003t}$
$1-\frac{0.012v}{g}={e}^{-0.003t}$
$1-{e}^{-0.003t}=\frac{0.012}{g}v$
$v=\frac{g}{0.012}\left(1-{e}^{-0.003t}\right)$
$\frac{dx}{dt}=\frac{g}{0.012}\left(1-{e}^{-0.003t}\right)$
$dx=\frac{g}{0.012}\left(1-{e}^{-0.003t}\right)dt$
Integrating,

We have step-by-step solutions for your answer!

raefx88y
Solution:
Given, mass of the ball, $m=4kg$
air resistance, $=0.015v$
$t=3.4$ seconds
Now, speed at the ball at the bottom
$v=u+>$
$=0+9.8×3.4$
$=33.32\frac{m}{s}$
Resistance $=0.015v$
$=0.015×\left(33.32\right)$
$=0.5\frac{m}{{s}^{2}}$
$h=u+{y}_{2}g+2$ NSk $h=0+\frac{1}{2}\left(9.8-0.5\right)×{3.4}^{2}$
$h=53.754m$
Height of the building is 53.754m

We have step-by-step solutions for your answer!

karton

Mass of the body m=4 kg, time taken to hit the ground t=3.7s and air resistance f=0.013v. Since the ball was dropped, the initial velocity u=0.
Force equation for the ball, F=ma=mg-f

We have step-by-step solutions for your answer!