Ask Your Resident Physicist Questions

Eh, every now and then, I try my hand at one.

 

-Nope, not a fan of coffee. Soda, on the other hand...
-Dragons would be both awesome and terrifying to see in real life.

 

Eh, not really. I'm not a fan of racing in general. Just doesn't appeal to me.

 

We could use one of two kinematic equations to solve this:
vf^2 = vi^2 + 2*a*d OR vf = vi + a*t, where vf is the bus' final velocity (what we're looking for), vi is its initial velocity, a is its acceleration, d is the bus' displacement (the distance down the hill it travels), and t is the time it takes for the bus to reach the sign at the bottom. a is dependent on the angle of the hill - specifically, a = g*sin(θ), where g is the acceleration due to gravity (9.81m/s^2). From the wording of the problem, we can assume vi = 47mph = 29.01 m/s and θ = 82 degrees.
So vf = sqrt((29.01m/s)^2 + 2*9.81m/s^2*sin(82)*d) OR vf = 29.01m/s + 9.81m/s^2*sin(82)*t. Both should give us the same result.
Unfortunately, we're not given d or t. If we don't have those, we cannot solve the problem.

 

vf = sqrt((29.01m/s)^2 + 2*9.81m/s^2*sin(82)*d) OR vf = 29.01m/s + 9.81m/s^2*sin(82)*t
If we use d = 24ft = 7.32m, then: vf = sqrt((29.01m/s)^2 + 2*9.81m/s^2*sin(82)*7.32m) = 31.37m/s = 70.17mph.
If we use t = 4.72min = 283.2s, then: vf = 29.01m/s + 9.81m/s^2*sin(82)*283.2s = 2780m/s = 6219mph.
It's worth noting that these results assume a constant acceleration and a perfectly flat hill. If we're being realistic, a bus traveling at 47mph would cover a distance of 24 feet in way less than 4.72 minutes. Also, a hill with an 82 degree gradient is really frickin' steep.

 

-My astrological sign is Virgo (I think), and apparently I'm a Rat.
-I'm generally indifferent to cats. In terms of species, tigers (particularly Siberian tigers) are pretty neat.

 

-I don't know if I've previously mebtuonedt this, but I'm an avid bowler.
-I enjoy baking from time to time. Does that count?
-To eat, my favorites are pretty bland (apples, oranges, grapes). To look at, the more exotic fruits (like dragonfruit) are interesting. For the veggies, that would be potatoes, but only because fries exist.

 

Without a doubt, cookies... though Tollhouse squares are a close second.

 

I haven't seen one in person (I don't think...), but I think they're pretty neat. I'd kinda like to see an active one in person someday. I particularly like the ones whose ash clouds produce lightning.

 

I know the basics. If you're asking me to explain it, I think I can give you a decent idea of what it is and how it works.