# How to find the time of two object passing each at opposite direction.

1. A ball is dropped from a height of 79 m. Simultaneously a ball is thrown upward from the ground at a velocity of 28 m/s. How much time passes until the balls are at the same height.

I need someone to check if my approach is correct.

Position of falling object
x =?
Δt =?
Xo = 79 m
Vo = 0 m/s
A = -9.8 m/s 2

X = Xo + Vo 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 =?
Xo = 0 m
Vo = 28 m/s
A = -9.8 m/s 2

X = Xo + Vo 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.

Related Introductory Physics Homework Help News on Phys.org
gneill
Mentor
Your approach is fine, and the result of 2.8s is good (at least to one decimal).

Keeping a few more decimal places in intermediate results would make your check of the answer more convincing So my answer is correct, right?

gneill
Mentor
So my answer is correct, right?
I believe that is what I stated...

Alrite thank you so much.

gneill
Mentor
Alrite thank you so much.
No problem. Cheers 