Real-Life Sidewalk Wheelies

Posted on June 9, 2013 by laura

Have you ever seen a car driving so fast – either in a movie or real life – that as it drives around the corner it tilts up on two wheels? That is so totally not a safe way to drive a car, but now some people are driving like that on purpose. It’s called “sidewalk skiing,” and it’s all the rage in the country of Saudi Arabia. As you can see in this crazy video, the cars lurch to one side then the other to get themselves up on two wheels, then all the riders in the car move around to balance their weight so the car stays balanced, while the driver steers to keep the car on its side. They seem to be going straight enough and fast enough to drive on a regular street, so maybe this isn’t a bad way to drive after all. However, you need other people in the car to balance it, so this will only work for carpool time.

Wee ones: If a 4-wheeled car starts skiing with just 2 wheels on the ground, how many wheels are up in the air?

Little kids: If 6 cars go out to sidewalk-ski, how many wheels are driving on the ground? Bonus: How many wheels do they all have in total?

Big kids: If you need to drive 62 miles an hour to tilt the car onto two wheels, and you’re going only 47 miles an hour, how much faster do you need to drive to do the stunt? Bonus: If you have 4 riders who each weigh 190 pounds, how many pounds of weight do you have handy to balance the car?

The sky’s the limit: The center of mass for a bunch of things on a straight line is the point where if you multiply each thing’s weight times its distance from the center, the total for all things on one side adds up to the total for all the things on the other side. If you have 3 riders in the car, A B and C, who weigh 140 pounds, 150 pounds and 200 pounds, plus their 40-pound pet dog, and they can each sit either 1 foot or 2 feet from the center of mass, who has to sit on which side and how far away to balance each other out?

Answers:
Wee ones: 2 wheels in the air.

Little kids: 12 wheels. Bonus: 24 wheels.

Big kids: 15 miles an hour faster. Bonus: 760 pounds.

The sky’s the limit: There are a few ways to balance it out. It balances if you put B, the 150-pounder, 2 feet to the left of center, the dog 1 foot to the left of center, and the other two riders 1 foot to the right of center (presumably one sitting in the other’s lap). The 150 weight times 2-foot distance gives you 300, and the dog 1 foot from center adds 40, yielding 340. If you seat the 140-pounder A and the 200-pounder C 1 foot to the right of center, they add 140 and 200, which also totals to 340. Another way is if the 200-pounder C and the 40-pound dog sit on to the left of center, with C 2 feet away and the dog 1 foot away. On the other side, the 150-pounder B would be 2 feet from center and the 140-pounder A would be 1 foot. Then both sides total 440.

Dog-Tired? Take the Train.

Posted on June 5, 2013 by laura

Most pet-owners are quick to tell you their dog or cat or bird or pot-bellied pig is very smart. They’re usually right, too – animals can be incredibly quick learners, and many have a great sense of direction for finding their way home. Even more interesting, some animals learn to travel like people to get places: There are a few dogs in the Russian city of Moscow who know how to ride the train! No one is sure exactly how the pups know when to get on and off at their regular stops, but somehow they do it. So if you’re ever lost on the Moscow Metro, a canine could point you the right way. Just remember to throw that dog a bone for the ride.

Wee ones: If your dog wants to ride 3 miles from the center of town, and then switches trains and rides another 2 miles, how many miles will your doggie ride?

Little kids: If there are 15 open seats on the train car, and 9 dogs get on and take seats as if they’re people, how many open seats are left? Bonus: If the dogs wait 14 minutes for the train, then take 3 minutes to get on, and then take a 6-minute ride, how long does their whole trip take?

Big kids: The dogs can wait 19 minutes for the speedy Express train or just 13 minutes for the slower Local – but the Express takes 22 minutes to arrive at their station while the Local takes 31. Which one will get the dogs home earlier, and by how many minutes? Bonus: A dog waits 8 minutes for her train and the ride home normally takes 3 times as long as that. If the train then drives at 1/2 its normal speed, how long in total till the dog gets home?

Answers:
Wee ones: 5 miles.

Little kids: 6 remaining seats. Bonus: 23 minutes.

Big kids: The Express will arrive 3 minutes earlier – in 41 minutes vs. 44. Bonus: 56 minutes, because the ride now takes 48 minutes instead of 24 (plus the 8-minute wait).

Cross-Country Choo-Choo

Posted on June 4, 2013 by laura

Back in the 1800′s, the fastest way to travel was by train, pulled by steam locomotive – but only between cities that were connected by tracks. There was no easy route across the U.S., as some stretches of mountain and desert were crossable only by horse-drawn wagon. Some people actually sailed all the way around South America instead. Either way the trip took weeks and cost a small fortune ($1,000, which was a lot back then). So imagine the excitement when two railroads connected their tracks to make one continuous train track from coast to coast. The Central Pacific company built eastward from California, while the Union Pacific built westward from the Missouri River. They met in Utah in May 1869, and on this day in 1876 the first train ever to cross the country reached San Francisco in just under 84 hours. Now we can fly it by plane in 6 hours, but compared to horse-drawn buggies, that train flew like lightning.

Wee ones: If a train has a locomotive, 4 passenger cars and a caboose, how many cars does it have?

Little kids: If the trip took 84 hours, how many more hours did it take than our 6-hour flight today? Bonus: If the track was completed in 1869 and the first train crossed it in 1876, how many years later was that?

Big kids: If that trip took 84 hours and we now fly it in 6, how many times as fast do we make the trip today? Bonus: The first trip by train took just under 84 hours. How many days of straight running did that take? (Your answer will involve a simple fraction…)

The sky’s the limit: Because the Union Pacific was coming from Omaha, Nebraska over easy plains while the Central Pacific had to blast through mountains, Union Pacific built many more miles of track. If for the first 4 months the CP built half as fast as the UP, but for the last month the CP matched the UP and they built at the same rate, how much of the 1600-mile track did each one build?

Answers:
Wee ones: 6 cars in total.

Little kids: 78 hours. Bonus: 7 years later.

Big kids: 14 times as fast. Bonus: 3 ½ days (because a half day, 12 hours, goes in 7 times).

The sky’s the limit: The UP built 4 months’ worth of track plus another month, for 5 months in total, but the CP built only 2 months worth followed by 1 month, for 3 months’ total. So of the 8 month-long chunks of track, the UP built 5. So they built 5/8ths of 1600 miles, or 1000 miles, while the CP built the remaining 600 miles. (For the history buffs, the actual numbers are 1,086 for the UP and 690 for the CP.)

Next Floor: Space!

Posted on May 23, 2013 by laura

Elevator rides are fun to begin with, especially when you jump right when it’s slowing down and you fly up higher than usual. But how would you like to take an elevator into space? Scientists think it may be possible. Basically it would use a very long rope attached to the ground here on Earth, with a “counterweight” of over 100,000 pounds at the other end way up in space. That weight would keep the rope tight because as Earth spins, it would sling the weight around, just like when you twirl a yo-yo around your head and the string stays tight. The counterweight would circle Earth in “geostationary orbit,” meaning it would stay above the same spot on Earth so you don’t have a crazy elevator ride on an angle. It all depends on finding a strong enough material for that cable – but as soon as we do, we’re pressing Up for the next ride.

Wee ones: If someday we build 4 space elevators, then 1 goes out of service for repairs, how many elevators are left running?

Little kids: The super-strong cable for the space elevator would be about 24,000 miles long. To compare, Earth is about 25,000 miles around. How many miles longer would the cable have to be to wrap all the way around Earth? (Hint: just think in chunks of a thousand.) Bonus: How much cable would you need to build 2 elevators?

Big kids: 100,000 pounds is a lot of weight. If a big car weighs about 4,000 pounds, how many cars would you have to strap together in space as the counterweight? Bonus: If the space elevator travels 240 miles an hour, how long would it take you to ride the 24,000 miles from the ground up to the top in space?

Answers:
Wee ones: 3 elevators left.

Little kids: 1,000 miles longer (1 thousand). Bonus: 48,000 miles (48 thousand).

Big kids: 25 cars. Bonus: 100 hours.

Give Me a Sign

Posted on May 16, 2013 by laura

Billboards are those big rectangular signs along the side of the highway, usually trying to talk you into buying something. Since they’re a good 50 feet above you, these signs are even bigger than they look – they’re 20, 30, or even over 40 feet wide. The size depends on the speed of the traffic: the faster you’re driving, the easier it has to be for people to read it, so the bigger the letters and pictures need to be. The signs along slower streets in town, called “posters,” are 22 feet wide, but the big “bulletins” along the highway are up to 48 feet wide. Now we have digital billboards that light up like a computer screen and change the picture every few seconds, showing drivers even more things they should buy. Either one works, as long as we read it quickly: the more important thing as a driver is to keep your eyes on the road.

Wee ones: Which one is wider, a 20-foot-wide poster or a 40-foot-wide billboard?

Little kids: If a billboard is 10 feet tall and the bottom is 50 feet off the ground, how many more of those same signs could you stack edge to edge below it? Bonus: If you want to climb up to that 50-foot sign but all you have is an 8-foot ladder, how many more feet does your ladder have to reach?

Big kids: If an adult’s face is 9 inches tall, and all objects on a billboard are 12 times life size, how tall is a face shown on a billboard? Bonus: These giant highway signs are about as big as a house. If the front of a house has a 15-foot-wide kitchen, a 6-foot-wide hallway, and an 18-foot-wide living room, which one is wider, the house or a 48-foot-wide highway billboard?

The sky’s the limit: Suppose as a prank you decide to climb up a billboard at night and wrap a string of lights around the edge. If you need exactly 82 feet of strung lights to cover all four sides, and the area of the billboard (length times width) is 400, what are the width and height of the billboard?

Answers:
Wee ones: The billboard is the bigger number.

Little kids: 5 more of those signs. Bonus: 42 more feet.

Big kids: 108 inches, or 9 feet! Bonus: The billboard would be wider if leaned up against the house – 48 feet vs. 39.

The sky’s the limit: It’s 25 by 16 feet. We know that the width and height have to add to 41, since those two sides will use up half the lights. Those same two numbers also multiply out to 400. You can use trial and error to test the factors of 400 numbers: 40 by 10 doesn’t work, nor does 20 by 20, but 16 by 25 does. Expressing this using algebra:
w + h = 41, so h=41-w
w x h = 400. Replacing h, you get
w x (41-w)=400
41w – w^2=400, or w^2-41w+400=0
…and then you still need trial and error to break it down into
(w-25) x (w-16)=0. So w=16 or 25.