Hello, I need help answering and explaining the question in the attached image. It includes the figures plus the question and the multiple choice answers. Thank you!

d.

Explanation:

Since the dart's initial speed v at angle has both vertical and horizontal components v₀sinθ and v₀cosθ respectively, the vertical component of the speed continues to decrease until it hits the target. It's displacement ,s is gotten from

s = y - y₀ = (v₀sinθ)t - 1/2gt² where y₀ = 0 m

y - 0 = (v₀sinθ)t - 1/2gt²

y = (v₀sinθ)t - 1/2gt²

which is the parabolic equation for the displacement of the dart.

Note that the horizontal component of the dart's velocity does not change during its motion.

Since the target falls vertically, with initial velocity u = 0 (since it was stationary before the string cut), it's displacement ,s' is gotten from

s' = y - y₀' = ut - 1/2gt² where y₀' = initial height of target above the ground

= (0 m/s)t - 1/2gt²

= 0 - 1/2gt²

y - y₀' = - 1/2gt²

y = y₀' - 1/2gt²

which is the parabolic equation for the displacement of the target.

The equation for both the displacement of the dart and the target can only be gotten if we considered vertical motion. So, the displacement component of both the dart and target are both vertical.

So, the answer is d.

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