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Question

Quiet enjoying this, a morning workout to get everyone awake.

I am standing on top of a 1,250m high tower, but suddenly it disappears. After stating, ‘Damn, this could be bad’, I plummet to Earth. 16s later, I hit the ground, but what speed am I going?

Ignore Air Friction, and Wind effects.

As always, this problem is solvable by our Geniuses out there.

1400 hours today, as it is a pencil cruncher, but you do need to say how you got the answer. No marks for just the answer.

Don’t worry. As luck would have it, I was wearing my super trainers today, so I will survive the drop, and will return on Monday to provide the next workout.

There are 3 ways to solve this equation; 2 Equations and the practical solution.

The practical solution is to find a building of suitable height, and step off, and measure the speed on landing. Do not jump, as that will affect the figures.

There is an equation that links, distances, mass and speed with acceleration, but that would require to know my mass. There are other equations as well, as demonstrated below. Some of you may have thought of using v=d/t, but this is only for constant speed, not for accelerated movement.

The easiest equation is a=((v-u)/t). Acceleration is a, v is the final speed, u is the starting speed, and t is the time taken. Since this is on Earth (I did not suggest anywhere else), the acceleration is due to gravity, as I said do not include air friction. a=9.8m/s/s. u=0 as the tower disappeared. Had I jumped, that would have created a starting speed, and changed the distance. Time is given as 16s and v is what we want to find.

Substitute to get:
a=(v-u)/t
9.8=(v-0)/16
v-0=9.8*16
v=156.8 m/s

I would also have taken 160 as that indicates you took gravity as 10.

My motivation for doing this, since I do not force you to answer or read this, if you don't know and don't want to know, then just ignore it, if you do know, and do want to show off you do, get yourself 2 pts.

There are a lot of silly questions on this website, and the same questions come up a lot. I have seen the "Why is the sky blue" question 6 times in 3 weeks.

This is a fun chance for you to use all that stuff you picked up while sitting in maths thinking "Why the hell will I need to know that c=2piR"

Have fun fellow geniuses, and remember, if it were not for the ignorant masses, you would not be able to call yourself better than anyone else.

Answer 1

Ahh, since gravity accelerates you at 9.8 meters per second, per second, and you accelerated for 16 seconds, can't you just multiply 9.8 by 16 to get velocity after 16 seconds? Who cares how high the tower is...

156.8 m/s

Answer 2

hmm, "standard" distance eqn:

s = (1/2) a t^2 [note a=9.8 m/s^2 ... t is given by "16"]
s = (1/2) * 9.8 * 16^2
s = 4.9 * 256 = 1254 meters ... pretty close to 1250
so no inconsistencies yet

v = at = 9.8 * 16 = 156.8 m/sec is "how fast" you hit the ground

"a" = acceleration [9.8 m/s^2 is earth-gravity]
"t" = time
"s" = distance
"v" = velocity


... the skill-level you indicate in your narrative indicates that you have sufficient neuronal capbility to solve this problem ... what is your motivation??

Answer 3

You've travelled 1,250m in 16s, giving an average speed of 78.125m/s. You started at 0m/s, so, as acceleration is uniform in the absence of air resistance etc, your final velocity must be double the average. 2 x 78.125 = 156.25m/s.

Just spotted this is identical to Clon's solution. Doh!

Answer 4

Simplest (mathetically, not conceptually) solution.

Average speed = 1250 / 16 = 78.125 m/s
Assuming that your initial vertical speed = 0 m/s
Impact speed = 2 x 78.125 = 156.25 m/s.

Answer 5

You fall at a rate of 78.125 meters per second,(1250/16)
speed is 4687.5 meters per minute

1250/16=78.125, 78.125x60=4687.5

shoot - looking at the geniuses that have answered, guess i'm wrong! lol

Answer 6

v^2=u^2+2*gx
=(0^2) + 2(9.8*1250)
=24500

v=156.52m/s

Answer 7

175 mph

Answer 8

what the hell are you talking about man i can not understand anything and i hope i am not so much intelligent or is it about your way that has not made me to understand it

Answer 9

v = sqrt (2gh)

g = about 10

h = 1,250

thus v is about 158 m/s.

Answer 10

u'll reach terminal velocity, which i think is round 140mph and no faster