solve this question using the quadratic equation

Question

A projectile moves vertically upward such that its distance s (in feet) above the ground is given by s=100+200t-16ft^2. Determine when the projectile will hot the ground (to 0.1 s)

Answer 1

x = {-b ± √ (b² - 4ac) } / 2a

 

f(x) = -16t² +200t +100, a = -16, b = 200, c = 100

 

x = {-200 ± √ (40000 - 4(-16)(100))} / -32

x = {-200 ± √ (40000 + 6400)} / -32

x = {-200 ± √ 46400} / -32

x ≈ {-200 ± 215.4} / -32

x ∈ {12.98, -0.48}

 

Time cannot be negative (at least not here) so so the projectile hits the ground after 12.98 seconds.