Question

You could walk across the Lehigh River if you had a pair of water-walking boots shaped like canoes. If each boot is 25cm high and 35cm wide how long must they be to support a 75kg person?
I can't figure it out :(

Answer 1

In order to support a 75 kg person, 75 kg of water must be displaced by the boots. Can you figure out what volume of water has a mass of 75 kg? You need to know the density of water.

Answer 2

the density is 1000

Answer 3

Right, 1000 kg/m^3. So how many m^3 would have a mass of 75 kg?

Answer 4

uhm idk..

Answer 5

Density of a substance is calculated using\[D=\frac{ m }{ V }\]You know the density (1000 kg/m^3) and the mass (75 kg). Are you able to rearrange the equation and solve for volume?

Answer 6

so mass x density

Answer 7

To get V out of the denominator, multiply both sides by V, giving\[DV=m\]Then to isolate V, divide both sides by D, giving\[V=\frac{ m }{ D }\]Noe calculate V

Answer 8

uhm 0.75?

Answer 9

Not quite. To divide a number by 1000, move the decimal three places to the left. Or use a calculator.

Answer 10

oh it's .075

Answer 11

sorry . that was a typo

Answer 12

Correct. So the total volume of both boots must be 0.075 m^3. So what must be the volume of one boot?

Answer 13

uhm would i divide by 2?

Answer 14

Exactly

Answer 15

ok so 0.0375

Answer 16

Perfect, the volume of one boot must be 0.0375 m^3. Assume the boot is shaped like a big shoe box (i.e. a rectangular prism). Do you know how to calculate the volume of a rectangular prism?

Answer 17

l x w x h

Answer 18

Exactly. So the question gives h and w, and you know what the volume has to be. Can you rearrange\[V=l \times w \times h\]and solve for l? Don't forget that the dimensions of the boot must be in meters in order for the volume to be in m^3.

Answer 19

l=v/w(h)

Answer 20

Perfect. Plug in the values and solve.

Answer 21

ok so i got 0.0525

Answer 22

Not what I get. Try again.\[l=\frac{ V }{ w \times h } = \frac{ 0.0375 }{ \left( 0.25 \right) \left( 0.35 \right) } = ?\]

Answer 23

oh its 0.43

Answer 24

Tada. Well done. Now to answer the question. How long do the boots have to be?

Answer 25

uhm wait i thought that was how long they needed to be because that's the length.

Answer 26

Sorry, I didn't mean to confuse you. You have indeed figured out how long they have to be. Your answer is in meters. The other dimensions are given in cm. It might be a good idea to answer in cm.

Answer 27

so 43cm

Answer 28

Good work!

Answer 29

thank u ! :) i appreciate it

Answer 30

You're welcome.