I don't even know how to begin this.
You drop a rock into a deep well. You can't see the rock's impact at the bottom, but you hear it after 7 seconds. The depth of the well is _____ feet. Ignore air resistance. The time that passes after you drop the rock has two components: the time it takes the rock to reach the bottom of the well, and the time that it takes the sound of the impact to travel back to you. Assume the speed of sound is 1100 feet per second.
Note: After seconds the rock has reached a depth of feet where d=16t^2
I don't know what is required . . . let's find SOME of the unknown.
I will use the data above,
T + t = 7 - - - - (1)
Let T = time going down, in seconds
t = time going up, in seconds
d = depth of the well, feet
d = (acceleration of the rock)(Time going down)^2 = 16T^2 - - - - (2)
also, d = (speed of sound)(time going up) = 1100t - - - - (3)
equate (2) and (3)
16T^2 = 1100t
t = 16T^2/1100 - - - - (4)
substitute (4) in (1),
T + t = 7, that is t = 16T^2/1100
T + 16T^2/1100 = 7, cross-multiply
1100T + 16T^2 = 7700,rearrange them
16T^2 + 1100T - 7700 = 0,
it is now quadratic in T, can you solve it now?