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I need someone to check if my approach is correct.

Position of falling object

x =?

Δt =?

X

_{o }= 79 m

V

_{o }= 0 m/s

A = -9.8 m/s

^{2}

X = X

_{o}+ V

_{o}Δt + .5a (Δt)

^{2}

X = 79 m + 0m/s (Δt) + .5(-9.8 m/s

^{2)}(Δt)

^{2}

X = 79 m - 4.9 m/s

^{2}(Δt)

^{2}

Position of elevating object

x =?

Δt =?

X

_{o }= 0 m

V

_{o}= 28 m/s

A = -9.8 m/s

^{ 2}

X = X

_{o}+ V

_{o }Δt + .5a (Δt)

^{2}

X (Δt) = 0m + 28m/s Δt + .5a (Δt)

^{2}

X (Δt) = 28 m/s (Δt) + .5(-9.8 m/s

^{2}) (Δt)

^{2}

X (Δt) = 28 m/s (Δt) – 4.9 m/s

^{2 }(Δt)

^{2}

To find the time, we need to set both the equation equal to each other.

79 m – 4.9 m/s

^{2}(Δt)

^{2 }= 28 m/s (Δt) - 4.9 m/s

^{2}(Δt)

^{2}

79m = 28 m/s (Δt)

2.8 s = Δt

Then I replace 2.8 for t in both of the equation and check if my time is correct

X = 79 m – 4.9 m/s

^{2}(Δt)

^{2}

X = 79 m – 4.9 m/s

^{2}(2.8 s)

^{2}

X = 79 m - 4.9 m/s

^{2}(7.84s

^{2})

X = 79 m - 38.416 m

X = 40.6 m

X = 28 m/s (Δt) – 4.9 m/s

^{2}(Δt)

^{2}

X = 28 m/s (2.8s) - 4.9 m/s

^{2}(2.8 s)

^{2}

X = 78.4 m - 38.416 m

X = 40 m

The answer is approximately the same.