PS.1.2 Shooting the Apple

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A diagram showing the projectile gun's position relative to the apple hanging on the tree.

An apple is suspended a height \(\displaystyle h \) above the ground. A physics demo instructor has set up a projectile gun a horizontal distance \(\displaystyle d \) away from the apple. The projectile is initially a height \(\displaystyle s \) above the ground. The demo instructor fires the projectile with an initial velocity of magnitude \(\displaystyle v_0 \) just as the apple is released. Find \(\displaystyle \theta _0 \), the angle at which the projectile gun must be aimed in order for the projectile to strike the apple. Ignore air resistance.

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