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On a hot summer day in the state of Washington while kayaking, I saw several swimmers jump from a railroad bridge into the Snohomish River below. The swimmers stepped off the bridge, and I estimated that they hit the water 1.5 s later. (a) How high was the bridge? (b) How fast were the swimmers moving when they hit the water? (c) What would the swimmers' drop time be if the bridge were twice as high?

(a) 11.04 $\mathrm{m}$(b) 14.71 $\mathrm{m} / \mathrm{s}$(c) $t=2.12 \mathrm{s}$

Physics 101 Mechanics

Chapter 2

One-Dimensional Kinematics

Motion Along a Straight Line

Hope College

University of Sheffield

McMaster University

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So in this problem you saw sweepers jumping from a railroad bridge into a river below. And you estimated that the time they took her to hit the water was 1.5 seconds. Okay, What else? Well, the first item of the problem. You want to know how I was a bridge? So we want to find out. Do X, Delta X. How high was the breach? Well, let's see. The movement that you solved was you saw a person that's represented this box for free, falling a river below. So you want to find out distance the height off the reef, off the off the bridge. You know that if they are free falling, they are under gravity acceleration off nine point 81 meters per second squared. And, you know, they begin up dressed So the initial velocity is zero. Well, what equation can we use to discover the height you need your The only information you have is the time and ah, gravity deceleration. So the only equation we know the related space as a function of time is just x x x equals zero less visitor T plus G G square divided by two. Well, X minus X zero is just the difference in position. V zero is the initial velocity. We know it's zero. So that sounds reduce the difference in position that we want the height of the bridge. It's going to be just nine point 81 divided by two times 1.5 square. That is the time. So let's see, that's calculate this. So after calculating this week, No, that the height off the bridge. It's just 11 point 04 meters. Okay, this is the answer for the first item. What? The second night and no, we want to know how fast the streamers I'm moving when they hit the water. Okay, so basically, we just want to find out their final velocity off the swimmers. This is the I can be. Well, we still have the time. Time was 1.5. We still have to gravity the separation night point anyone. And now we have the displacement. There was just 11.4 Okay, so we have time, displacement, gravity. We have almost everything. So we're going to use the easiest off the equations. That is the velocity as a function off time. So v zero going to be zero Daddy's Danish velocity plus nine point 81 times 1.5 This is equals two to let's see if let's see another car lor uh, the final velocity It's going to be 14 point 71 meters per second is the answer for the second item and the third eye tonight and see well what they don't know, we're what would this simmers? Okay, okay, so in the itin See, we want to know what will be the time the drop time of the swimmers if the bridge has twice this size the height So if the bridge I think she has twice the height two times height recalculated This is going to be just 22 0.0 h and we want to find the time. OK, so using the same equation off the first the first part first item we can put in here 22 points your weight It costs too 9.81 divided by two times T square. So the square is going to be 4.5 hopes let's see four point five, then the square root off T It's going to be two point 12 seconds. This is the final answer

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