Equation help.

[Gareth56]

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

[ydoaPs]

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.

[Gareth56]

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.

[Country Boy]

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.

[Gareth56]

Yes, it does matter but you should have been able to see what to do.

 

Oh sorry "Sir"

[Country Boy]

I assume that you were bowing deeply when you said that!