Question

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?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

y do u put h as zero?

Answer 5

im confused.

Answer 6

can yu show us what yu plugged in for 4)

Answer 7

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

Answer 8

oohhh i get it

Answer 9

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

Answer 10

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.

Answer 11

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

Answer 12

or put in our calculator

Answer 13

isolate "t"

Answer 14

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

Answer 15

no
i jus dun understand how to solve 4)

Answer 16

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

Answer 17

...

Answer 18

did you understand why h = 0 ?!!!

Answer 19

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

Answer 20

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]

Answer 21

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

Answer 22

yupp

Answer 23

I'm glad you understood :)

Answer 24

ty