Physics: Falling Objects?!?

Question

A freely falling object requires 1.10 s to travel the last 34.0 m before it hits the ground. From what height above the ground did it fall?

It just doesn't seem like there's enough information to get an answer.

Answer 1

here is a hint, because im sure this will answer your question.

its in free fall that means the acceleration is 9.8m/s^2....now you shuold have enough info

Answer 2

For the last 34 meters,

S = VT + (1/2)gT^2

where

S = 34 meters (given)

V = velocity of the object at a point 34 meters from the ground

T = time = 1.1 sec. (given)

g = acceleration due to gravity = 9.8 m/sec^2 (constant)

Substituting appropriate values,

34 = V(1.1) + (1/2)(9.8)(1.1)^2

Solving for V,

V = (34 - 4.9)/1.1

V = 26.45 m/sec.

The second formula to use is

V^2 - Vo^2 = 2gs

where

Vo = initial velocity = 0 (in the absence of any other data, this is assumed to be initially dropped)

s = distance travelled by the ball until it is 34 meters from the ground

and all the other terms have been previously defined.

Substituting values,

(26.45^2) - 0 = (2)(9.8)(s)

Solving for "s",

s = (26.45)^2/(2 * 9.8)

s = 35.69

Therefore,

Total distance travelled by the object = 34 + 35.69 = 69.69 meters

Answer 3

this may not be the most efficient way to solve this, but here's how I'd do it.

First, figure out the velocity the object is at when it begins the last 34.0 m of its fall:

change of X = 1/2 (v initial + v final)t, so

34.0m = 1/2 (v initial + v final) times 1.10s

so 68.0m/1.10 s = v initial + v final.

Now, remember that the acceleration of gravity is 9.80m/s^2, so therefore

v initial plus v final = v initial + v initial + 9.80m/s^2 times 1.10s

so 61.8 m/s = 2(v initial) + 10.8m/s.

so v initial = 25.5 m/s

NOW, go back to the equation above, but now your initial v is starting from rest (when object was dropped) until it reaches the 25.5m/s (when it starts the last 34.0m of its fall)

so change of x = 1/2(0.0m/s + 25.5m/s) times (25.5m/s divided by 9.8m/s^s)

= 33.2m

(this works because once we know the speed it is at during the fall, 25.5m/s, we know how long a TIME it has been falling, because we know the acceleration of gravity)

So it had already fallen 33.2 meters before it got to that 34.0 meter section of the fall, so it was dropped from 33.2 + 34.0 = 67.2 meters height.