Speed of Light

Today I learned that the first calculations on tge speed of light came when someone noticed that the eclipses cased by Jupiter's moons were appearing several minutes later then the were predicted to. I must research this further to see if there is a way i can turn this into a classroom problem.

Multi-part geometry problem

One side of a right scalene triangle is 100. The perimeter is 240. A similar triangle has a scale factor of 3:5 (new:old). Find the perimeter of the new triangle. Find both possible sets of solutions for the other two sides of the new triangle.

The Math of "The Martian" Sol 98

These are the first two messages that Watney received today. Translate them from ASCII:

Message 1:

434e48414b52565232544c4b32505448464452505250344c4f4e474d5347

Message 2:

4c4e4348686578696469744f4e525652434d502c4f50454e46494c452d2f7573722f6c69622f686162636f6d6d2e736f2d5343524f4c4c54494c4944584f4e4c465449533a32414145352c4f565257525431343142595453575448444154415745274c4c534e444e58544d53472c5354414e44494e56494557344e45585450494332304d494e41465452544853444f4e45

The Math of "The Martian" Sol 97 (2) Solution

Sol 97 (2) SOLUTION

Mark instructed NASA to time their transmissions so they arrived at the top of every hour, with their first transmission arriving at 11:00am. Which means the last transmission from NASA arrived at 5:00pm. Marks’s first note would have to be placed up at least 32 minutes before 11:00 am, so this entire conversation took at least 6 hours and 32 minutes.

ASCII conversions:

STATUS: 535441545553

HOWALIVE: 484F57414C495645

CROPS?: 43524F50533F

WESAW-SATLITE: 57455341572D5341544C495445

BRINGSJRNROUT: 4252494E47534A524E524F5554

SJRNRNOTRSPND: 534A524E534E4F545253504E44

WORKINGONIT: 574F524B494E474F4E4954

The Math of "The Martian" Sol 97 (2)

Sol 97 (2)

Mark has fixed the Pathfinder lander to communicate with earth! Although it will be tedious, the story states that earth and Mars are currently 16 light minutes apart. He can hand write messages on note cards and place them in view of the camera, getting a response is much more tricky. Mark has decided to tell NASA to use ASCII to spell messages. He placed then numbers 0 through 9, and the letters A through F in a circle around the lander. NASA can select one by pointing to the camera at it. The following is their’ first day’s worth of communication:

Mark: Spell with ASCII. 0-F at 21-degree increments. Will watch camera staring 11:00 my time. When message done, return to this position. Wait 20 minutes after completion to take picture (so I can write and post reply). Repeat process at top of every hour.

NASA: STATUS

Mark: No physical problems. All Hab components functional. Eating ¾ rations. Successfully growing crops in Hab with cultivates soil. Note: Situation not Ares 3 crew’s fault. Bad luck.

NASA: HOWALIVE

Mark: Impaled by antenna fragment. Knocked out by decompression. Landed facedown, blood sealed hole. Woke up after crew left. Bio-monitor computer destroyed by puncture. Crew had reason to think me dead. Not their fault.

NASA: CROPS?

Mark: Long story. Extreme botany. Have 126 m2 farmland growing potatoes. Will extend food supply, but not enough to last until Ares 4 landing. Modified rover for long-distance travel, plan to drive to Ares 4.

NASA: WESAW-SATLITE

Mark: Government watching me with satellites? Need tinfoil hat! Also need faster way to communicate. Speak&Spell taking all damn day. Any ideas?

NASA: BRINGSJRNROUT

Mark: Sojourner rover brought out, placed 1 meter due north of lander. If you can concoct it, I can draw hex numbers on the wheels and you can send me six bytes at a time.

NASA: SJRNRNOTRSPND

Mark: Damn. Any other ideas? Need faster communication.

NASA: WORKINGONIT

Mark: Earth is about to set. Resume 08:00 my time tomorrow morning. Tell family I’m fine. Give crew my best. Tell Commander Lewis disco sucks.

How long did this conversation take?

Convert NASA’s transmissions back into ASCII.

The Math of "The Martian" Sol 83 Solution

The Math of "The Martian" Sol 83

Mark is retrieving the Pathfinder space probe in hopes of fixing it’s radio so that he can communicate with earth. He is at Pathfinder’s landing site, but he needs to get the probe onto the roof of his rover. He has removed several parts of the probe that he won’t need, but it still has a mass of 200 kg. How much would that weigh on Earth? How much would that weigh on Mars?

He has decided that the best way to get it up to the top of the rover is to use rocks to build a ramp. After some small scale experiments he has determined that the best angle for the ramp will be 30 degrees. If the rover is 2.5m tall, how long will the base of the ramp be?

If the ramp is 1m wide, and the rocks in the area have a density of 3 g/cm^3, what is the upper limit of the mass of rocks must he move to create his ramp? How much does this weigh on Mars?