# Time of Free Fall

## Homework Statement

If a car rolls gently (v0 = 0) off a vertical cliff, how long does it take it to reach 73 km/h?

A helicopter is ascending vertically with a speed of 7.50 m/s. At a height of 110 m above the Earth, a package is dropped from a window. How much time does it take for the package to reach the ground? [Hint: The package's initial speed equals the helicopter's.]

## Homework Equations

Vf = Vi + at
d = Vi(t) + (.5)(a)(t)^2
t= Vf/a or Vf-Vi/a

## The Attempt at a Solution

For the first one : I set Vi at 0, Vf at 73, and a(acceleration) at 9.8. From there i did 73/9.8 to find the time when it is traveling 73 km/h, and got 7.44, which is obviously wrong. I'm guessing I have to find distance, but I'm not sure how.

For the second one: I set Vi at 7.5, d (distance) at 110, and a at 9.8. Then I used the Vf^2 formula to find Vf, which was 47. Then i did (47-7.5)/9.8 to get about 4 seconds, which was wrong.

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ideasrule
Homework Helper
For the first one : I set Vi at 0, Vf at 73, and a(acceleration) at 9.8. From there i did 73/9.8 to find the time when it is traveling 73 km/h, and got 7.44, which is obviously wrong.

For the second one: I set Vi at 7.5, d (distance) at 110, and a at 9.8. Then I used the Vf^2 formula to find Vf, which was 47. Then i did (47-7.5)/9.8 to get about 4 seconds, which was wrong.
Why 47 minus 7.5? In which direction was the package's initial speed (7.5 m/s)? In which direction was its final speed (47 m/s)?

Thanks a lot for the reply ideasrule.

So for the first one, I'm not really aware of what Vo = 0 means. I took it as initial velocity, but I may be wrong. And should Vf not be 73? I thought it should because that's the speed it will be traveling when the time is discovered.

For the second one, I can now see that the velocities should be added together, as they are traveling in the same direction. But the answer I get is higher, (54/9 compared to 39.5/9) when shouldn't it be getting smaller, since the speed is increasing? Any more hints would be greatly appreciated

For the first part, you have to keep in mind what units your using. If you do have Vo (where yes, the o typically stands for the conditions of that variable in it's initial state) in km/hr, then you would have to make sure that a and Vf are both in km/hr. It's clear that it's much simpler to just convert Vo to m/s. For b), you have to keep in mind the direction of the vectors. best way is to say up is "+" and down is "-". When using the equations you used, think about whether a value is - or +. For example, for d, if you say the initial point is 0, then the point at which it hits the ground is -110m, and therefore vf would be a negative value, and vi would be a positive value. So you are correct, just a little fuzzy in your vector notation. And yes, the time should increase. Look at the equation for t=(Vf-Vi)/a. if there is great difference between the final and initial velocities, the numerator gets bigger as this difference gets bigger, and t increases. Or you can just think: the acceleration changes the velocity over time, so the more the velocity is changed, the more time it takes.

Thanks so much guys I got the first one. But now I am sooo confused on the second one. I dont understand which numbers should be positive or negative, and im still not sure how to go about solving this. Any help?

Never mind i got it guys. Thanks so much!