fisico

Chatgpt:

We have two bodies:

A starts from the ground: , upwards.

B starts from height : , upwards.

Take upward as positive, ground at .
Motion under gravity :

y(t) = y_0 + v_0 t – frac12 g t^2

Body A (from ground)

At impact with the ground :

0 = 0 + v_1 t_A – frac12 g t_A^2

Non-zero solution:

t_A = frac{2v_1}{g}

Body B (from height )

For B at ground: :

0 = h + v_2 t_B – frac12 g t_B^2

We want them to hit the ground at the same time, so .
Substitute:

0 = h + v_2 left(frac{2v_1}{g}right) – frac12 gleft(frac{2v_1}{g}right)^2

0 = h + frac{2v_1 v_2}{g} – frac{2v_1^2}{g}

Solve for :

h = frac{2v_1^2}{g} – frac{2v_1 v_2}{g}
= frac{2v_1 (v_1 – v_2)}{g}

Insert , , and :

h = frac{2 cdot 80 cdot (80-50)}{10}
= frac{2 cdot 80 cdot 30}{10}
= frac{4800}{10}
= 480 text{m}

So the required height is:

boxed{h approx 480 text{m}}

(Using would give about .)

Ti s’di as te besh foto