Projectile Launched From a Shell
A shell is launched at 53 degrees above the horizontal. When it has reached its highest point, it launches a projectile at a velocity of 30 degrees above the horizontal relative to the shell. Let be the maximum height in meters above the ground that the projectile reaches. Find .
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1 solution
sin 5 3 ∘ = 1 5 0 v shell vertical v shell vertical = 1 5 0 sin 5 3 ∘ 0 = ( 1 5 0 sin 5 3 ∘ ) 2 + 2 g s shell vertical max s shell vertical max = 2 g ( 1 5 0 sin 5 3 ∘ ) 2 sin 3 0 ∘ = 1 0 0 v projectile verticle v projectile verticle = 1 0 0 sin 3 0 ∘ 0 = ( 1 0 0 sin 3 0 ∘ ) 2 + 2 g s projectile vertical max s projectile vertical max = 2 g ( 1 0 0 sin 3 0 ∘ ) 2 ⌊ T o t a l / 1 0 0 ⌋ = ⌊ 1 0 0 s projectile vertical max + s shell vertical max ⌋ = ⌊ 1 0 0 2 g ( 1 0 0 sin 3 0 ∘ ) 2 + 2 g ( 1 5 0 sin 5 3 ∘ ) 2 ⌋ = 8