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Why is the answer D?

Why is the answer D?-example-1
User Kopecs
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Step-by-step explanation:

Projectiles launched at complementary angles have the same range. Only option D has complementary angles (adds up to 90°).

We can prove this with kinematics.

First, find the time for a projectile to land:

Δy = v₀ t + ½ at²

0 = (v₀ sin θ) t + ½ (-g) t²

0 = v₀ sin θ − ½ g t

t = 2 v₀ sin θ / g

Now find the horizontal distance (range) traveled in that time:

Δx = v₀ t + ½ at²

Δx = (v₀ cos θ) (2 v₀ sin θ / g) + 0

Δx = 2 v₀² sin θ cos θ / g

Δx = v₀² sin (2θ) / g

If we replace θ with 90°−θ:

Δx = v₀² sin (2(90°−θ)) / g

Δx = v₀² sin (180°−2θ) / g

Δx = v₀² sin (2θ) / g

We get the same range.

User Torez
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