A stone dropped from the rest travels 113 feet in the first 2 seconds. How far will it have fallen at the end of 5 seconds? ( round the answer to the nearest in

Question

A stone dropped from the rest travels 113 feet in the first 2 seconds. How far will it have fallen at the end of 5 seconds? ( round the answer to the nearest integer) 

Answer 1

h(t) = -(a/2)t^2 = -113 = -(a/2)(2)^2 = -2a

a=113/2 = 56.5 ft/sec/sec deceleration.

at the usual gravity deceleration, it's a= -32 feet per sec per sec. In 2 seconds, without other factors, a stone would fall from rest -16(2)^2 = -64 feet

How did it fall 113 feet? Was there some down draft? wind blowing downward?

some vacuum below sucking the stone downward? In either event add in an initial velocity into the equation:

h(t) = -16t^2 + vo where vo is initial velocity

-113 = -16(2)^2 + vo(2)

2vo = (-113 + 64)/2 = - 49/2 = -24.5 feet per second

plug in t=5

h(5) = -16t^2 -24.5t = -16(5)^2 -24.5(5) = -400 - 122.5 = -522.5 feet in 5 seconds

the stone dropped 645 feet in 5 seconds. that's an exact number, not rounded

h(2) =-16(2)^2 -24.5(2) = -64-49= -113 feet in 2 seconds