How Long Does a Bolt Fall the Last 28% of 85 Meters?

[Gattz]

Homework Statement

A bolt is dropped from a bridge under construction, falling 85 m to the valley below the bridge. (a) In how much time does it pass through the last 28% of its fall? What is its speed (b) when it begins that last 28% of its fall and (c) when it reaches the valley beneath the bridge?

Homework Equations

No idea.

The Attempt at a Solution

I did .28 x 85 = 23.8 m. I also assumed g = 9.8 m/s^2, xinitial = 23.8, xfinal = 0, but I'm now lost. The five constant acceleration constants need v or t which I have neither.

 

[dariusphysics]

Homework Statement

A bolt is dropped from a bridge under construction, falling 85 m to the valley below the bridge. (a) In how much time does it pass through the last 28% of its fall? What is its speed (b) when it begins that last 28% of its fall and (c) when it reaches the valley beneath the bridge?

Homework Equations

No idea.

The Attempt at a Solution

I did .28 x 85 = 23.8 m. I also assumed g = 9.8 m/s^2, xinitial = 23.8, xfinal = 0, but I'm now lost. The five constant acceleration constants need v or t which I have neither.

does the question require you to take air resistance into account? Or should I assume that it's dropped in vacuum?

I won't tell you how to solve it, but I'll just give you a hint and some relavent equations. (As stated by the forum rules, we don't do your homework for you.)

Hint: Draw a speed-time graph. Assign variables to the unknown numbers.

Relavent equations:

a = (v-u)/t
v = d/t

Good thing to remember: Always draw the speed-time graph or velocity-time graph if you're unsure on how to solve a kinematics question. (just a rough sketch of it will do, you don't have to draw it accurately on graph paper)

 

[Gattz]

I believe I'm suppose to neglect air resistance. How could I draw a speed-time graph, if I don't have velocity or time? And what is "u" in the a = (v-u)/t equation?

 

[physicsface]

Well, first you might want to figure out the information for the first 72% of the fall - that will help you get the starting velocity when the bolt enters the final 28%, and from there you can find all the other information you need.

 

[Gattz]

Would a = -9.8 or +9.8?

Okay I did part b without doing part a if that is possible. First I flipped the problem upside down so the starting point is 0m and the bolt is falling up to 85m so that a = 9.8. I did v² = v_o² + 2a(x-x_o) to find v. So it's v²=0 + 2(9.8)(61.2-0). So v = 24.5m/s. That's part b.

But I'm confused on what part a is asking. Does it mean how much time elapsed during the last 28% of the fall or in my case the flight upward?

 

[physicsface]

Acceleration is technically -9.8 because it's in a downward direction, but your method looks sound to me. I mean, the problem is asking for speed anyway; therefore, you don't need the negative sign to indicate direction, so you're fine - but just be aware that if you come across something similar asking for velocity, it would be negative.

And yes, part a is asking how much time elapses during the final 28% of the fall.

 

[Gattz]

For part a I did x-x_o=v_ot + 1/2at². Plugging in I get

85-61.2=24.5t + 1/2(9.8)t² to get 4.9t² +24.5t - 23.8 = 0

Okay, that's nice, but when I tried doing quadratic formula, both my times come out to be negative. t = -1.32s and -3.68. What did I do wrong?

 

[physicsface]

I'm thinking maybe you made an error with the quadratic formula.

 

[Gattz]

My god, you are right, I made the answer to -4ac to negative. Ok so then the answer for a must be .8seconds. Does that sound too small? Also I found the answer for part c to be 33 m/s.

 

[physicsface]

No, that all sounds about right. :)

 

[Gattz]

Thanks so much physicsface! Great help!