An arrow is shot vertically upward at a rate of 280 feet per second. Use the projectile formula

h = - 16t2 + v0t

to determine at what time t (in seconds) the height of the arrow will be 200 feet.

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