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A-projectile-is-fired-with-velocity-v-o-such-that-it-passes-through-two-points-both-a-distance-h-above-the-horizontal-show-that-if-the-gun-is-adjusted-for-the-maximum-range-of-the-separation-of-two




Question Number 177548 by peter frank last updated on 07/Oct/22
A projectile is fired with velocity(v_o )  such that it passes through two  points both a distance(h) above the  horizontal.show that if the gun is adjusted  for the maximum range of the  separation of two position is  d=((v_o (√(v_o ^2 −4gh)))/g)
Aprojectileisfiredwithvelocity(vo)suchthatitpassesthroughtwopointsbothadistance(h)abovethehorizontal.showthatifthegunisadjustedforthemaximumrangeoftheseparationoftwopositionisd=vovo24ghg
Answered by blackmamba last updated on 07/Oct/22
y=y_o +x tan θ −((gx^2 )/(2v_o ^2  cos^2 θ))   since θ=45° ,y=h , y_o =0  then h=0+x tan 45°−((gx^2 )/(2v_o ^2  cos^2 45°))  b= x−((gx^2 )/v_o ^2 ) or x^2 −(v_o ^2 /g).x +(v_o ^2 /g)h =0  x_1 +x_2 = (v_o ^2 /g)  ⇒(x_1 −x_2 )^2 = (x_1 +x_2 )^2 −4x_1 x_2   ⇒d^2 = ((v_o ^2 /g))^2 −4(((v_o ^2  h)/g))  ⇒d=(√(((v_o ^2 /g))^2 (v_o ^2 −4gh)))  ⇒d =((v_o  (√(v_o ^2 −4gh)))/g)
y=yo+xtanθgx22vo2cos2θsinceθ=45°,y=h,yo=0thenh=0+xtan45°gx22vo2cos245°b=xgx2vo2orx2vo2g.x+vo2gh=0x1+x2=vo2g(x1x2)2=(x1+x2)24x1x2d2=(vo2g)24(vo2hg)d=(vo2g)2(vo24gh)d=vovo24ghg
Commented by Tawa11 last updated on 07/Oct/22
Great sir
Greatsir
Answered by Spillover last updated on 07/Oct/22
x=v_o cos θt  y=v_o sin θt−(1/2)gt^2   R=((v_o ^2 sin 2θ)/g)           θ=(π/4)  x=((v_o t)/( (√2)))       y=((v_o t)/( (√2)))−(1/2)gt^2   x^2 −((v_o ^2 x)/g)+((v_o ^2 h)/g)=0  x_1 =(v_o ^2 /(2g))−(v_o /(2g))(√(v_o ^2 −4gh))   x_2 =(v_o ^2 /(2g))−(v_o /(2g))(√(v_o ^2 −4gh))   d=x_2 −x_1   d=(v_o /g)(√(v_o ^2 −4gh))    ★★★
x=vocosθty=vosinθt12gt2R=vo2sin2θgθ=π4x=vot2y=vot212gt2x2vo2xg+vo2hg=0x1=vo22gvo2gvo24ghx2=vo22gvo2gvo24ghd=x2x1d=vogvo24gh
Commented by peter frank last updated on 07/Oct/22
more clarification please step 3?  and how θ=(π/4)? diagram please?
moreclarificationpleasestep3?andhowθ=π4?diagramplease?

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