application task type question

[cootcoot]

a spider man soars from the top of a building, that is 48.4 metres above the ground and then descends towards the evil sandman below. spider man's height, h metres above the ground, at times t seconds can be modelled by the equation: h = 50 +(a/(t-25)), where 0=t and a is a constant.

so that was fine

then it said

after 24 seconds, spider man becomes distracted by batman and reaches the ground exactly 2 seconds later. for the second part of the journey, the relationship between h and t can be modelled by the equation: h= a(t-24)^2  + c

a) find the values of a and c.

i asked my teacher, and he just gave me the answers without actually showing me how to do it. so i know the answer is a= -2.5 and c=10. but i don't know how...

i got one equation ... 0=4a +c   but thats all i got to...

any help would be lovely!!!

[Glockmeister]

Ok, I think the first thing to note is that the from the first equation, does not equal the from the second equation. (They should've used a different letter)

Now given our first equation



We can say that when as this is before the start of spider man doing his thing.







So we know that the first equation is:



From here we need to find the height at 24 seconds (i.e ) as this is the point common to both curves.







Therefore, we can substitute (24,10) into the second equation





We can then also substitute (26,0) into the equation.

[Collin Li]

Substitute (0, 48.4) into:





Substitute (26, 0) into:

[Mao]

...
typing.

lol

[Glockmeister]

I'm copying you lol

[Collin Li]

Oh I see. This stupid question uses two meanings for . I assumed that the way they used twice meant that they already crafted the equations to be consistent.

[Glockmeister]

That's what I though initially first, and I probably would've have gone with that chain of thought if I didn't read the answer before I started doing it.

Should've used a different letter.

[cootcoot]

thank you so much for that!!