February 22, 2007,
Woo! Engineer's Week!
1. Assuming that this savings accounts will not accrue any interest over the time period specified, Tim should have enough to buy the iPhone plus 424 dollars left over (total of $1,024). Work:
Starting on day 1 with 1 dollars, the amount in the account doubles with a period of 10 days, until day 101. This means the account doubles 10 times (days 11, 21, 31, 41, 51, 61, 71, 81, 91, and 101). Therefore total = 1 * 2^10, or 1024.
2. Assuming the document starts downloading at the same time that Tim starts walking, tim will be struck by the bus (he will have traveled 1.5 feet in front of the bus before the download is over). Work:
First, solve for time to download the 75 kb file at 9 kb/s. 75 - 9 * t = 0, giving t = 8 1/3 seconds. Using that amount of time multiplied by Tim's velocity of 4.5 ft/sec, we get 8 1/3 * 4.5 = 37.5 feet traveled. 36 - 37.5 = -1.5 ft. (a.k.a. ouch). Luckily, as Tim is both an engineer and an apple user, he has the strength of a thousand men, and recovers in time for the next problem.
3. Assuming that Tim has decided to go to his local vacuum park, and therefore will not encounter any lift or drag due to air resistance, the now obsolete iPhone will travel about 45.19 meters. Work:
First, find the vertical (Vy) and horizontal (Vx) components of the phone velocity (V0). Vy = V0 * sin 30 = 11 m/s, Vx = V0 * cos 30 = 19.053 m/s. We now need to solve for the amount of time it takes the phone to hit the ground. Looking at only vertical components, we see gravity acting downwards at 9.81 m/s/s, the initial velocity of 11 m/s, and the initial height of 1.5 m. Solving for time, we get the equation -9.81/2 * t^2 + 11 * t + 1.5 = 0. Using the quadratic formula to solve, we get t = (-11 +- sqrt(11^2 - 4 * -4.905 * 1.5)) / 2*-4.905. We can throw out the negative t, leaving us with a time elapsed of approximately 2.372 seconds. Then, we simply multiply the horizontal velocity by the time elapsed before the phone hits the ground, and find how far the phone traveled 2.372 s * 19.053 m/s = 45.19 m.
At least, that's how I remember math/physics. It's only been 3 years, and it's starting to fade fast.
Well, if I'm wrong, at least I spent my lunch break productively.
Also, by the way, even though the calendar is the best thing ever, and everyone should buy at least one, it appears to be missing a reference to Engineers Week. I think it's time for a angry letter writing campaign against calendar making companies.
--Greg
