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Question Number 48194 Answers: 1 Comments: 1

A body of mass 0.1kg dropped from a height of 8m onto a hard floor bounces back to a height of 2m. Calculate the change of momentum. If the body is in contact with the floor for 0.1s then what is the force exerted on the body? [g=10ms^(−2) ]

$${A}\:{body}\:{of}\:{mass}\:\mathrm{0}.\mathrm{1}{kg}\:{dropped}\:{from} \\ $$$${a}\:{height}\:{of}\:\mathrm{8}{m}\:{onto}\:{a}\:{hard}\:{floor} \\ $$$${bounces}\:{back}\:{to}\:{a}\:{height}\:{of}\:\mathrm{2}{m}. \\ $$$${Calculate}\:{the}\:{change}\:{of}\:{momentum}. \\ $$$${If}\:{the}\:{body}\:{is}\:{in}\:{contact}\:{with}\:{the} \\ $$$${floor}\:{for}\:\mathrm{0}.\mathrm{1}{s}\:{then}\:{what}\:{is}\:{the} \\ $$$${force}\:{exerted}\:{on}\:{the}\:{body}? \\ $$$$\left[{g}=\mathrm{10}{ms}^{−\mathrm{2}} \right] \\ $$

Question Number 48193 Answers: 1 Comments: 0

In the equation ax^2 +bx+c=0 one root is square of orther.without solving the equation.prove that c(a−b)^3 =a(c−b)^3

$${In}\:{the}\:{equation}\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$${one}\:{root}\:{is}\:{square}\:{of}\: \\ $$$${orther}.{without}\:{solving} \\ $$$${the}\:{equation}.{prove}\:{that} \\ $$$${c}\left({a}−{b}\right)^{\mathrm{3}} ={a}\left({c}−{b}\right)^{\mathrm{3}} \\ $$

Question Number 48187 Answers: 0 Comments: 0

The data arranged below in the form of a table was obtained for a motor cyclist of total mass 120kg traveling from Sun city towards Delta state. velocity/ms^(−1) 00 20 40 50 50 60 70 85 time,t/s 00 5 10 12 20 35 40 45 i) plot a graph of velocity(y−axis) against time(x−axis) ii) Detemine the acceleration of the cyclist for the first part of the motion iii) Calculate the pull of the engine during the first 12.5s if this section of the road is horizontal and friction with all other forces is negligible. iv)what is the momentum change during the first 12.5^(th) second v) detemine the kinetic energy of the cyclist at the 37.5^(th) second vi) for how long is the resultant force zero on the cyclist during motion?

$$\mathrm{The}\:\mathrm{data}\:\mathrm{arranged}\:\mathrm{below}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\mathrm{of}\:\mathrm{a}\:\mathrm{table}\:\mathrm{was}\:\mathrm{obtained} \\ $$$$\mathrm{for}\:\mathrm{a}\:\mathrm{motor}\:\mathrm{cyclist}\:\mathrm{of}\:\mathrm{total}\:\mathrm{mass}\:\mathrm{120}{kg}\:{traveling}\:{from}\: \\ $$$${Sun}\:{city}\:{towards}\:{Delta}\:{state}. \\ $$$$ \\ $$$${velocity}/{ms}^{−\mathrm{1}} \:\:\mathrm{00}\:\:\:\:\:\mathrm{20}\:\:\:\:\:\mathrm{40}\:\:\:\mathrm{50}\:\:\:\:\:\mathrm{50}\:\:\:\:\mathrm{60}\:\:\:\mathrm{70}\:\:\:\:\mathrm{85} \\ $$$$\:\:\:\:\:{time},{t}/{s}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{00}\:\:\:\:\:\mathrm{5}\:\:\:\:\:\:\:\mathrm{10}\:\:\:\:\mathrm{12}\:\:\:\:\:\mathrm{20}\:\:\:\mathrm{35}\:\:\:\:\mathrm{40}\:\:\:\:\mathrm{45} \\ $$$$\left.{i}\right)\:{plot}\:{a}\:{graph}\:{of}\:{velocity}\left({y}−{axis}\right)\:{against}\:{time}\left({x}−{axis}\right) \\ $$$$\left.{ii}\right)\:{Detemine}\:{the}\:{acceleration}\:{of}\:{the}\:{cyclist}\:{for}\:{the}\:{first}\:{part}\:{of}\:{the}\:{motion} \\ $$$$\left.{iii}\right)\:{Calculate}\:{the}\:{pull}\:{of}\:{the}\:{engine}\:{during}\:{the}\:{first}\:\mathrm{12}.\mathrm{5}{s} \\ $$$${if}\:{this}\:{section}\:{of}\:{the}\:{road}\:{is}\:{horizontal}\:{and}\:{friction}\:{with}\:{all} \\ $$$${other}\:{forces}\:{is}\:{negligible}. \\ $$$$\left.{iv}\right){what}\:{is}\:{the}\:{momentum}\:{change}\:{during}\:{the}\:{first}\:\mathrm{12}.\mathrm{5}^{{th}} \:{second} \\ $$$$\left.{v}\right)\:{detemine}\:{the}\:{kinetic}\:{energy}\:{of}\:{the}\:{cyclist}\:{at}\:{the}\:\mathrm{37}.\mathrm{5}^{{th}} \:{second} \\ $$$$\left.{vi}\right)\:{for}\:{how}\:{long}\:{is}\:{the}\:{resultant}\:{force}\:{zero}\:{on}\:{the}\:{cyclist} \\ $$$${during}\:{motion}? \\ $$

Question Number 48182 Answers: 1 Comments: 0

Question Number 48178 Answers: 1 Comments: 1

find ∫ ((sin(πx))/(3 +cos(2πx)))dx

$${find}\:\:\int\:\:\:\frac{{sin}\left(\pi{x}\right)}{\mathrm{3}\:+{cos}\left(\mathrm{2}\pi{x}\right)}{dx} \\ $$

Question Number 48177 Answers: 0 Comments: 2

find lim_(x→0) ∫_(x+1) ^(2x+1) ((tarctan(t^2 +1))/(1+(1+t^2 )^2 ))dt

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\int_{{x}+\mathrm{1}} ^{\mathrm{2}{x}+\mathrm{1}} \:\:\:\frac{{tarctan}\left({t}^{\mathrm{2}} +\mathrm{1}\right)}{\mathrm{1}+\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dt} \\ $$

Question Number 48175 Answers: 1 Comments: 2

calculate lim_(x→0) ∫_x ^x^2 ((ln(1+t))/(sin(t)))dt

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\frac{{ln}\left(\mathrm{1}+{t}\right)}{{sin}\left({t}\right)}{dt} \\ $$

Question Number 48174 Answers: 1 Comments: 1

find lim_(n→+∞) ∫_0 ^n sin(((πx)/n))dx .

$${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\int_{\mathrm{0}} ^{{n}} \:\:\:{sin}\left(\frac{\pi{x}}{{n}}\right){dx}\:. \\ $$

Question Number 48173 Answers: 1 Comments: 2

calculate ∫ ((arctan(x))/(√(1+x^2 )))dx

$${calculate}\:\int\:\:\frac{{arctan}\left({x}\right)}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 48172 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((sin(2cos(x^2 +1)))/(1+x^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}\left(\mathrm{2}{cos}\left({x}^{\mathrm{2}} +\mathrm{1}\right)\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 48171 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((sin(cosx))/(x^2 +3))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}\left({cosx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$

Question Number 48170 Answers: 1 Comments: 1

calculate ∫_0 ^∞ ((cos(sin(x^2 )))/(1+2x^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({sin}\left({x}^{\mathrm{2}} \right)\right)}{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 48165 Answers: 0 Comments: 0

In a version of millikan experiment it is a charged droplet of mass 1.8x10^(−15) kg just remain stationary where the p.d between the plates which are 12mm apart is 150v. If the droplet suddenly gain an extra electron. Find (a) the acceleration of the droplet (b) the p.d to bring it back to stationary possition. PLEASE HELP

$$\mathrm{In}\:\mathrm{a}\:\mathrm{version}\:\mathrm{of}\:\mathrm{millikan}\:\mathrm{experiment}\:\mathrm{it}\:\mathrm{is} \\ $$$$\mathrm{a}\:\mathrm{charged}\:\mathrm{droplet}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}.\mathrm{8x10}^{−\mathrm{15}} \mathrm{kg} \\ $$$$\mathrm{just}\:\mathrm{remain}\:\mathrm{stationary}\:\mathrm{where}\:\mathrm{the}\:\mathrm{p}.\mathrm{d}\: \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{plates}\:\mathrm{which}\:\mathrm{are}\:\mathrm{12mm} \\ $$$$\mathrm{apart}\:\mathrm{is}\:\mathrm{150v}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{droplet}\:\mathrm{suddenly} \\ $$$$\mathrm{gain}\:\mathrm{an}\:\mathrm{extra}\:\mathrm{electron}.\:\mathrm{Find} \\ $$$$\:\:\:\left(\mathrm{a}\right)\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{droplet} \\ $$$$\:\:\:\left(\mathrm{b}\right)\:\mathrm{the}\:\mathrm{p}.\mathrm{d}\:\mathrm{to}\:\mathrm{bring}\:\mathrm{it}\:\mathrm{back}\:\mathrm{to}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{stationary}\:\mathrm{possition}. \\ $$$$\boldsymbol{\mathrm{P}}\mathrm{LEASE}\:\mathrm{HELP} \\ $$

Question Number 48169 Answers: 0 Comments: 1

let u_n =∫_0 ^∞ cos(nx^2 )dx and v_n =∫_0 ^∞ sin(nx^2 )dx with n >0 1) calculste u_n and v_n 2)find nsture of Σ(u_n +2v_n ) and Σ (u_n ^2 +4v_n ^2 ) 3)find nature of Σ(u_n +2v_n )^2

$${let}\:{u}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{cos}\left({nx}^{\mathrm{2}} \right){dx}\:{and}\:{v}_{{n}} =\int_{\mathrm{0}} ^{\infty} {sin}\left({nx}^{\mathrm{2}} \right){dx}\:{with}\:{n}\:>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{u}_{{n}} {and}\:{v}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{nsture}\:{of}\:\Sigma\left({u}_{{n}} +\mathrm{2}{v}_{{n}} \right)\:{and}\:\Sigma\:\left({u}_{{n}} ^{\mathrm{2}} \:+\mathrm{4}{v}_{{n}} ^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{3}\right){find}\:{nature}\:{of}\:\Sigma\left({u}_{{n}} +\mathrm{2}{v}_{{n}} \right)^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 48161 Answers: 1 Comments: 1

f(z)=((1−z)/(1+z)) u(x,y)=.. v(x,y)=..

$${f}\left({z}\right)=\frac{\mathrm{1}−{z}}{\mathrm{1}+{z}} \\ $$$${u}\left({x},{y}\right)=.. \\ $$$${v}\left({x},{y}\right)=.. \\ $$$$ \\ $$$$ \\ $$

Question Number 48156 Answers: 2 Comments: 1