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3x+12=5x-21
-5x -5x
-2x + 12 = -21
-12 -12
-2x=-33
x = 16.5
Time is 16.75 seconds when the arrow reaches 200 ft
Step-by-step explanation:
- Step 1: Find time at height of 200 ft
Height = 200 ft
v = 280 ft/s
Projectile formula, h = -16t² + vt
⇒ 200 = -16t² + 280t
⇒ 16t² - 280t + 200 = 0
⇒ 2t² - 35t + 25 = 0 (dividing by common factor 8)
Using quadratic formula to find t
t = (35 ±√35² - 4×2×25)/2×2
t = (35 ±√1225 - 200)4 = 35 ± 32.02/4
∴ t = 67/4 or 3/4
t = 16.75 seconds
