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American football uses a field that is 100 yd long, whereas a regulation soccer ficld is 100 $\mathrm{m}$ long. Which field is longer, and by how much (give yards, meters, and percent)?

$9 \mathrm{yd}, 8 \mathrm{m}, 9 \%$

Physics 101 Mechanics

Chapter 1

Introduction, Measurement, Estimating

Physics Basics

Mariane L.

September 27, 2020

Cornell University

Simon Fraser University

Hope College

Lectures

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look, this question states American football uses a field that is 100 yards long, whereas regulation soccer field is 100 meters long, which field is larger and by how much, give the difference in yard's meters in percent. So I wrote down here. What we were given were given that the length of the football field which I wrote as Elsa Beth, is 100 yards the length of the soccer field. Elsa S is 100 meters and I also wrote the conversion between meters and yards. Since we need to in order to compare them, we need them in the same unit, so one meter is equal to 1.9 yards already. Just by looking at this, since the meter is bigger than a yard and we have 100 yards and 100 meters. We know that the soccer field is going to have to be larger than the football field, but we have to actually show by how much larger is it in both meters and and feet. So let's go ahead and do it and I'm sorry, not in feet in yards, so let's go ahead and do it in yards first So we have the soccer field length minus the football field Link. Oh, right is equal too. Well, the soccer field is in meters, but we wanted in yards for going to find our answer and yards. So need to multiply this by the conversion between meters and yards and 1.9 yards for every one meter current meters. They're not yours. 1.9 yards for every one meter gray. Okay. And then we're going to subtract from that 100 yards. Okay, well, 100 meters times 1.9 yards per meter is going to be 109 yards. 109 minus 100 is going to give us a total good night yards. Okay, so the soccer field is nine yards larger than a football field. Well, let's find that in meters. No, we could take l s minus lf converted back two meters. But why not just convert the yards into meters? We already know the conversion between yards and meters. So we're gonna take nine yards. We're going to multiply that by the conversion between meters and yards. And that's going to give us, uh, well, first of all. It's just right. What? This is l s minus. Lf right is equal to nine yards, which we're now converting into meters. Well, they're for everyone. Niedere, there is 1.9 yards. Right? Okay. And if you go ahead and carry that out, take nine. Divided by 1.9 you get It's about 8.257 But since 100 has just one significant digit, we can only report to one significant digits since that's the highest order of accuracy that we have. So we're goingto round that off toe eight. So it's going to be eight meters, okay? And it also wants to know by what percentage is the soccer field larger than the football field. So that percentage percent larger, right? We need to take the amount. The soccer field is larger. So l s minus. L s divided by the size that we're comparing into, which is a less. And then we multiply that by who? There's a multiplication here. Multiply that by 100% to convert that ratio into percentage. Okay. And if you do that l s minus. Lf we've already found to be nine yards right. If you take nine yards and you divide it by 100 you multiply that by, um 100 then you get nine percent.

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