Gareth56 Posted November 18, 2007 Share Posted November 18, 2007 Does anyone know what the steps are to get "h" at just one side of the "=" sign? It's an equation from a physics book whih I just can't work out how the answer h is arrived at. t1 = 0.69s & t2 = 2.37s g =9.81m/s h =(h+0.5gt1^2)/t1)t2 - (0.5gt2^2) The answer is h = 8.02m Many thanks G56 Link to comment Share on other sites More sharing options...
ydoaPs Posted November 18, 2007 Share Posted November 18, 2007 Does anyone know what the steps are to get "h" at just one side of the "=" sign? It's an equation from a physics book whih I just can't work out how the answer h is arrived at. t1 = 0.69s & t2 = 2.37s g =9.81m/s h =(h+0.5gt1^2)/t1)t2 - (0.5gt2^2) The answer is h = 8.02m Many thanks G56 Given: t1=0.69s t2=2.37s g=9.81m/s2 [math]h=\frac{(h+0.5g{t_1}^2)t_2}{t_1}[/math] Multiply both sides by t1 and distribute the t2. [math]ht_1=ht_2+0.5g{{t_1}^2}t_2[/math] Get all your terms with the h variable to one side. [math]ht_1-ht_2=0.5g{{t_1}^2}t_2[/math] Factor out h. [math](t_1-t_2)h=0.5g{{t_1}^2}t_2[/math] Divide both sides by the coefficient of h. [math]h=\frac{0.5g{{t_1}^2}t_2}{t_1-t_2}[/math] Now, you just have to plug in your given values. Link to comment Share on other sites More sharing options...
Gareth56 Posted November 19, 2007 Author Share Posted November 19, 2007 Many many thanks. Given:t1=0.69s t2=2.37s g=9.81m/s2 [math]h=\frac{(h+0.5g{t_1}^2)t_2}{t_1}[/math] Multiply both sides by t1 and distribute the t2. [math]ht_1=ht_2+0.5g{{t_1}^2}t_2[/math] Get all your terms with the h variable to one side. [math]ht_1-ht_2=0.5g{{t_1}^2}t_2[/math] Factor out h. [math](t_1-t_2)h=0.5g{{t_1}^2}t_2[/math] Divide both sides by the coefficient of h. [math]h=\frac{0.5g{{t_1}^2}t_2}{t_1-t_2}[/math] Now, you just have to plug in your given values. Does it matter that (0.5gt2^2) isn't included in the above solution because when plug in the numbers I should get 8.02m but for some reason I don't. Link to comment Share on other sites More sharing options...
Country Boy Posted November 23, 2007 Share Posted November 23, 2007 Yes, it does matter but you should have been able to see what to do. You have h=(h+0.5gt1^2)/t1)t2 - (0.5gt2^2) which can't be correct- there are more ")" than "(". Assuming you meant h=((h+0.5gt1^2)/t1)t2 - (0.5gt2^2), multiplying out that first term on the right, is h= h(t2/t1)+ 0.5gt1t2- 0.5gt2^2. Now subtract that first term from both sides h- h(t2/t1)= 0.5gt1t2- 0.5gt2^2 factor h out on the left: h- h(t2/t1)= h(1- t2/t1)= h(t1/t1- t2/t1)= h(t1-t2)/t1. (That's only the left side!) On the right, we can factor out 0.5, g, and t2: 0.5gt1t2- 0.5gt2^2= 0.5gt2(t1- t2). (That's only the right side.) Going back to the entire equation we now have h(t1-t2)/t1= 0.5gt2(t1- t2). Finally, multiply both sides by t2/(t2-t1). Of course, (t1-t2)/(t2-t1)= 1 so we have h= 0.5gt1t2. Link to comment Share on other sites More sharing options...
Gareth56 Posted November 25, 2007 Author Share Posted November 25, 2007 Yes, it does matter but you should have been able to see what to do. Oh sorry "Sir" Link to comment Share on other sites More sharing options...
Country Boy Posted November 26, 2007 Share Posted November 26, 2007 I assume that you were bowing deeply when you said that! Link to comment Share on other sites More sharing options...
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