Gravity and acceleration simple calculation

[forrestuv]

With this formula for distance calculation with gravity acceleration:

distance = 1/2 × acceleration × time^2 + intial speed × time

what Initial Acceleration does an object need to touch the ground in 3secs from 7meters of heigth?
what's the formula for that?

thx

 

[Doc Al]

what Initial Acceleration does an object need to touch the ground in 3secs from 7meters of heigth?

I assume you want the initial speed, not acceleration. The acceleration of a falling body is fixed at 9.8 m/s^2.

what's the formula for that?

That formula will do. Just solve for the initial speed.

 

[forrestuv]

ops.. yes I need the initial speed..how to obtain that from the formula I posted?I'm a real noob in math :(

 

[Doc Al]

It's just a bit of algebra. Take a stab at it.

For a start, if you had A = B + C, how would you solve for C?

 

[forrestuv]

C=a-b ? :)

 

[Doc Al]

C=a-b ? :)

Exactly. So rearrange your formula accordingly.

 

[forrestuv]

distance = 1/2 × acceleration × time^2 + intial speed × time

ok so:

intial speed × time = distance - (1/2 × acceleration × time^2)

then:

initial speed = (distance - (1/2 × acceleration × time^2)) / time

is it right? :)

 

[forrestuv]

in my case:

h=7 mt
t=3 secs
g=9.8

initial speed = (distance - (1/2 × acceleration × time^2)) / time

initial speed= (h- (1/2 × g × t^2)) / t

(7-(0.5x9.8x9)) / 3

(7-44.1) / 3 = -12.3666

can you check if it is correct please ? :)

 

[Doc Al]

can you check if it is correct please ? :)

Yes, it's correct. The reason why it's negative is that you have to throw the object upwards for it to take that long to fall 7m. (If you just dropped it would take only 1.2 seconds to hit the floor.)

In your equation, you took down as positive.

 

[forrestuv]

thxxxxxx!
I appreciated your help very very much :)

 

[forrestuv]

Now I would like to obtain something impossible to calculate for me :)
I need to know the min Initial speed needed to have, at a certain time a distance greater than a number.

example:
if I throw a ball at an initial speed of 12 I want to be sure that at 2 secs the distance is greater than 8.
is it possible?

science fiction for me eheh :)

 

[forrestuv]

alternatively:

Giving a fixed Initial Speed, If I want to double the distance at which the object will be at a certain time, how much should I increase time of?