1. ## Antiderivative.

A stone is dropped from CT Tower, 450m above the ground.
If the stone is thrown downward with a speed of 5m/s,
How long does it take to hit the ground...

I thought the answer is so simple just ,,,450/5=90s but it is not..

Please show me how to get t=9.09s

2. Originally Posted by camherokid
A stone is dropped from CT Tower, 450m above the ground.
If the stone is thrown downward with a speed of 5m/s,
How long does it take to hit the ground...

I thought the answer is so simple just ,,,450/5=90s but it is not..

Please show me how to get t=9.09s
The equation is,

h(t)=-16t^2+5t+450

Solve,

-16t^2+5t+450=0
For positive root.

3. I think the equation should be like this:

h(t)=-4.9t^2-5t+450

because I got the answer that I want.

I appreciate that Mr. PerfectHacker

4. Originally Posted by camherokid
A stone is dropped from CT Tower, 450m above the ground.
If the stone is thrown downward with a speed of 5m/s,
How long does it take to hit the ground...

I thought the answer is so simple just ,,,450/5=90s but it is not..

Please show me how to get t=9.09s
I think i got a different answer from TPH. I think that's because he worked in feet when the question has measurements in meters. here are the steps:

the acceleration due to gravity in meters is 9.8 m/s^2, so our acceleration function is:

a(t) = -9.8 ........since we are falling (moving in the negative direction)
now our velocity function is v(t) = int{a(t)}dt = int{-9.8}dt = -9.8t + C
now the initial velocity is -5, so
v(0) = -9.8(0) + C = -5
=> C = -5
so v(t) = -9.8t - 5

our position function is given by
s(t) = int{v(t)}dt = int{-9.8t - 5}dt = -4.9t^2 - 5t + C
our initial position is 450 m above ground, so
s(0) = -4.9(0)^2 - 5(0) + C = 450
=> C = 450
so s(t) = -4.9t^2 - 5t + 450

we want t when s(t) = 0
=> -4.9t^2 - 5t + 450 = 0
t = [5 +/- sqrt(25 + 8820)]/-9.8
=> t = -10.11s or t = 9.09s
t cannot be negative, so t = 9.09s

5. Originally Posted by camherokid
I think the equation should be like this:

h(t)=-4.9t^2+5t+450

because I got the answer that I want.

I appreciate that Mr. PerfectHacker
you won't get the answer you want with that equation, the 5t should be negative, otherwise, you'll get t = -9.09 and 10.11 and our answer should be +9.09 as you said

6. Hello, camherokid!

A stone is dropped from CT Tower, 450m above the ground.
If the stone is thrown downward with a speed of 5m/s,
how long does it take to hit the ground?
The general (metric) formula is: .h .= .ho + vot - 4.9t²

. . where h
o is the initial height and vo is the initial velocity.

We are given: .h
o = 450, vo = -5

The function is: .h .= .450 - 5t - 4.9t²

Solve h = 0: .4.9t² + 5t - 450 .= .0
. . . . . . . . . . . . . . . . . . . . . . .______________
. . . . . . . . . . . . . . . . . . -5 ± √5² - 4(4.9)(-450)
Quadratic Formula: . t .= .---------------------------- . .9.09 seconds
. . . . . . . . . . . . . . . . . . . . . . . . 2(4.9)

7. Just a quick comment as to WHY the 5 should be negative.

All of you are working in a coordinate system where the ground is the origin and +y is upward.

The initial position (450 m) is positive because it is above the origin and + is upward. The intial velocity is negative because the ball is being thrown downward. And the acceleration is negative because the weight acts in a downward direction.

ALWAYS choose and label a coordinate system!!

-Dan