a projectile is launched straight up from the ground with an initial velocity of 120 ft/s. if acceleration…

a projectile is launched straight up from the ground with an initial velocity of 120 ft/s. if acceleration due to gravity is -16 ft/s², after about how many seconds will the object reach a height of 200 ft?\nh(t)=at² + vt+h₀\n1.0 s\n1.7 s\n2.5 s\n8.0 s

a projectile is launched straight up from the ground with an initial velocity of 120 ft/s. if acceleration due to gravity is -16 ft/s², after about how many seconds will the object reach a height of 200 ft?\nh(t)=at² + vt+h₀\n1.0 s\n1.7 s\n2.5 s\n8.0 s

Answer

Answer:

C. 2.5 s

Explanation:

Step1: Identify values

$a=-16$, $v = 120$, $h_0=0$, $h(t)=200$

Step2: Substitute into formula

$200=-16t^{2}+120t + 0$

Step3: Rearrange to quadratic form

$16t^{2}-120t + 200=0$

Step4: Divide by 8

$2t^{2}-15t + 25=0$

Step5: Factor quadratic

$(2t - 5)(t - 5)=0$

Step6: Solve for t

$2t-5 = 0$ gives $t=\frac{5}{2}=2.5$; $t - 5=0$ gives $t = 5$. The value $t = 2.5$ is among the options, so the answer is 2.5 s.