Time of Free Fall Homework Answers

[Trizz]

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
Vf^2 = Vi^2 + 2ad
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.

 

[ideasrule]

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.

Check your units.

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)?

 

[Trizz]

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

 

[KaiserBrandon]

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.

 

[Trizz]

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

 

[Trizz]

Never mind i got it guys. Thanks so much!