- #1

- 127

- 5

r

^{2}=x

^{2}+y

^{2}

r2=x2+y2

So knowing that in 9.8 metres above ground it will take 1 second for an object to fall, I tried to find how many metres in the X direction an object must cover in 1 second before it falls 9.8 metres by

x2=r2 - y2

& y2 = r - 9.8

r = 6 371 000

thus x = 11 174.6 m/s ??

it's incorrect because if we use the formula derived from matching force from centripetal acceleration and gravitational acceleration at height r, it does not match:

( geometric proof shows that v-u / v = Dr & D=vt

plug and simplify, v-u=v2t/r, & a = v-u/t thus a= v2/r)

Since a = g = 9.8, then V = (sqrt) ar = (sqrt) 9.8 x 6 371 000 = 7901.63... m/s