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Question Number 178582 by Best1 last updated on 19/Oct/22
show that Range of the ff projection   obtained by algebric expression  R=(((ucosθ)(usinθ)+(√((usinθ)^2 +2gh)))/g)   help me please
showthatRangeoftheffprojectionobtainedbyalgebricexpressionR=(ucosθ)(usinθ)+(usinθ)2+2ghghelpmeplease
Commented by Best1 last updated on 18/Oct/22
please help me
pleasehelpme
Commented by Ar Brandon last updated on 18/Oct/22
dimension of (sinθ^2 )≠dimension of 2gh=M^2 T^(−2)   Check question.
dimensionof(sinθ2)dimensionof2gh=M2T2Checkquestion.
Commented by Best1 last updated on 19/Oct/22
i corrected it now help me
icorrecteditnowhelpme
Answered by Ar Brandon last updated on 18/Oct/22
For horizontal displacement  u_x =ucosθ ⇒x=u_x t  ⇒R=(ucosθ)t ⇒t=(R/(ucosθ)) ...(i)  For vertical displacement  y=u_y t+(1/2)at^2   ⇒h=(usinθ)t−(1/2)gt^2  ⇒gt^2 −2(usinθ)t+2h=0  ⇒t=((2usinθ±(√(4u^2 sin^2 θ−8gh)))/(2g))  ⇒t=((usinθ+(√(u^2 sin^2 θ−2gh)))/g) ...(ii)  (i)=(ii)  ⇒(R/(ucosθ))=((usinθ+(√(u^2 sin^2 θ−2gh)))/g)  ⇒R=(((usinθ)(ucosθ)+ucosθ(√(u^2 sin^2 θ−2gh)))/g)
Forhorizontaldisplacementux=ucosθx=uxtR=(ucosθ)tt=Rucosθ(i)Forverticaldisplacementy=uyt+12at2h=(usinθ)t12gt2gt22(usinθ)t+2h=0t=2usinθ±4u2sin2θ8gh2gt=usinθ+u2sin2θ2ghg(ii)(i)=(ii)Rucosθ=usinθ+u2sin2θ2ghgR=(usinθ)(ucosθ)+ucosθu2sin2θ2ghg
Commented by Best1 last updated on 18/Oct/22
is this the same as (((ucosθ)(usinθ)+(√(sinθ^2 −2gh)))/g)???
isthisthesameas(ucosθ)(usinθ)+sinθ22ghg???
Commented by Ar Brandon last updated on 18/Oct/22
I think this isn′t correct as the dimensions   aren′t the same.
Ithinkthisisntcorrectasthedimensionsarentthesame.

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