A cannonball is fired into the air. It's height, h, in metres after t seconds is given by the relation:
h=-4.6 (t-7.5)^2+285
a) what is the maximum height reached by the cannon and what time is this reached.
b) what was the initial height of the cannon?
c) what is the height of the cannon after 10.5 seconds?
d) how long is the cannon in the air?

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- mathmate

Do you just want just the answer or wnat to know how to find it?

- anonymous

Can you show me how to find it please with the ans

- y2o2

h = -4.6t²+69 t+26.25
the vertex of this function is the the time of maximum height
time of maximum height = -b/2a = 7.5
maximum height = -4.6(7.5)²+69(7.5)+26.25 = 285 meters
2)
initial height (t = 0) = 26.25 meters
3)
after 10.5 sec. (t = 10) = 243.6 meters
4)
time in air (h = 0)
t = 15.37

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## More answers

- anonymous

y do u put h as zero?

- anonymous

im confused.

- anonymous

can yu show us what yu plugged in for 4)

- y2o2

this ball will reach a maximum heigh (h)
then it returns back the same height (-h)
so it's total value = 0

- anonymous

oohhh i get it

- y2o2

BTW..this will be from the position of projection , not the surface of the cannon

- mathmate

The answer to part a is already given in the way the formula is expressed:
h=-4.6(t-7.5)^2+285
is in the vertex form. It shows that the vertex (highest or lowest point) is at the position (7.5,285), or a height of 285 after 7.5 seconds.

- anonymous

can yu put the equation where yu hav to isolste it
so we kno wht to rite

- anonymous

or put in our calculator

- anonymous

isolate "t"

- y2o2

actually I can't find anything confusing here
is the problem with expanding of the brackets ?!

- anonymous

no
i jus dun understand how to solve 4)

- anonymous

like how do u isolate "t" to find the time?

- anonymous

...

- y2o2

did you understand why h = 0 ?!!!

- anonymous

yeah we understand that, we just dont get how to put the "t" on one side of the equation, and the rest on the other side of the equation

- y2o2

well, as h = 0
then
h = -4.6 (t-7.5)²+285 = 0
-4.6 (t-7.5)² = -285 [divide by -4.6]
(t-7.5)² = 61.95 [approx.]
t-7 = 8 or t-7 = -8 [by taking +ve and -ve square root]
t = 15 or t = -1 [refused answer bec. t is never -ve]

- anonymous

thank you :D
charmi - u get it now? :P

- anonymous

yupp

- y2o2

I'm glad you understood :)

- anonymous

ty

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