Algebra help?

Question

solve by whatever method seems easiest to you. leave answers in simplest radical form.


1. The distance an object falls is directly proportional to the square of the time it has been falling. After 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 feet?

show work

Answer 1

call s = distance in feet
a = acceleration in feet / sec
t = time in seconds

s1 = 1296
t1 = 6
s2 = 2304
t2 = desired quantiuty

s = 1/2 at^2
/********************/
s1 = 1/2 a(t1)^2 => a = 2s1/(t1^2)
s2 = 1/2a(t2)^2=> a = 2s2/(t2^2)

same "a"
2s2/(t2^2) = 2s1/(t1^2)
[mult both sides by (t1*t2)^2 ]

t1^2 * (2s2) = t2^2 * (2s1)

t2^2 = t1^2 * (s2/s1) = 6^2 * 2304/1296
= 36 * 2034/1296 = 6* 2034/216 = 2304/36
t2^2 = 64
t2 = sqrt(64) = 8 sec


jeeeeze, I'm verbose



lololol

Answer 2

1296 = a/2 x 6 x 6
a/2 = 36
2304 = a/2 x t x t = 36 x t squared = 36 x 64
t=8
It will take 8 seconds
distance = 1/2 acceleration x time squared

Answer 3

The first sentence translates to
d = kt^2, where k is a constant whose value we can discover by using the given data.
Substitute the information given in the second sentence, and from the resulting equation we find k.

Using this value, substitute the information given in the third sentence and solve for t. I guess you can do that yourself, but AFTER you've done so, check below.









1296 = k*36
k = 36

When d = 2304,
2304 = 36t^2
t = 8

Answer 4

36 k = 1296 feet
k = 36
2304 = 36. x2
x2= 64
x=8 sec

Answer 5

3 pts on the graph
the equation has the form x=a*t^2

(0,0)
(6,1296)
(x,2304)

at 6 seconds

1296=a*(6^2)==> a = 36

for 2304'

2304=36*t^2

t= sqrt(2304/36) = 8

Answer 6

approx. 10.67 seconds


try cross multiplying (proportion)

6/1296 = x/2304 (then cross multiply)

(2304 x 6)= (1296 x X) (divide both sides by 1296)

(13824)/1296= 10.67 seconds..



got it?

Answer 7

11.28 seconds

1296divided by 6=216 ft per second
2304 divided by 216 =11.28 seconds

Answer 8

I like the phrase "show work".

Have you ever done pro bono work?