Projectile motion in 1 dimension problem

[toddler]

Hi, having trouble with the following problem:

A stone is thrown vertically upward from a bridge 30.0m high at an initial velocity of 15.0 m/s . How long will it take for the stone to hit water?


I set it up first by writing my givens down:
initial velocity = 15.0 m/s.
distance (x) = 30 m ( I'm not sure if its positive or negative since its coming back down)
Acceleration = -9.8 m/s squared (negative because its force coming down against gravtiy)

used kinematic equation : X= Intial velocity (time) + 1/2 at squared

i'm not getting the answer 4.44 that I am supposed to be getting..pleast help

 

[Astronuc]

used kinematic equation : X= Intial velocity (time) + 1/2 at squared

That's part of it.

Let's think about what is happening.

The stone is launched vertically with an intial velocity 15 m/s. So the stone travels upward until it stops, because it is decelerating with gravity.

What is that time?

Then the stone falls, in the same amount of time, back to the bridge. It must be then traveling at 15 m/s downward (it's falling) past the bridge (elevation where it started), and then continuing falling another 30 feet (the height of the bridge above the water).

 

[toddler]

my teacher said that if i make Acceleration a negative (-9.8), then i have to make the distance X negative also, which would be (-30) ... or you can make both positive,...as long as they are set up with the same sign, it will work out...

is this true?

 

[Astronuc]

my teacher said that if i make Acceleration a negative (-9.8), then i have to make the distance X negative also, which would be (-30) ... or you can make both positive,...as long as they are set up with the same sign, it will work out...

is this true?

Not in all cases. If the object was just falling, e.g. one drop a rock, then the distance would be negative if one used x = -1/2 g t². BTW, this is relative meaning the - sign indicates a decrease in elevation.

In the case where an object has an initial vertical velocity, it is gaining elevation (altitude) as it decelerates. In this case, the distance x, would be positive, that is until the projectile falls back to its initial elevation and continues to fall, as is the case in this problem.

The other approach would be to determine the height of the projectile at its maximum (and the time that it takes), then determine the time that it would fall from that point to the point of interest.

 

[toddler]

thank you astronuc, you cleared up the distance portion for me, i can visualize in my head now...but for the A=9.8, when is it negative and when is it positive...i'm still unsure about that