the projectile motion of an object can be modeled using (s(t)=gt^{2}+v_{0}t + s_{0}), where (g) is the…

the projectile motion of an object can be modeled using (s(t)=gt^{2}+v_{0}t + s_{0}), where (g) is the acceleration due to gravity, (t) is the time in seconds since launch, (s(t)) is the height after (t) seconds, (v_{0}) is the initial velocity, and (s_{0}) is the initial height. the acceleration due to gravity is (- 4.9 m/s^{2}). a rocket is launched from the ground at an initial velocity of 39.2 meters per second. which equation can be used to model the height of the rocket after (t) seconds? (s(t)=-4.9t^{2}+39.2) (s(t)=-4.9t^{2}+39.2t) (s(t)=-4.9t^{2}+39.2t + 39.2) (s(t)=-4.9t^{2}+39.2t-39.2)

the projectile motion of an object can be modeled using (s(t)=gt^{2}+v_{0}t + s_{0}), where (g) is the acceleration due to gravity, (t) is the time in seconds since launch, (s(t)) is the height after (t) seconds, (v_{0}) is the initial velocity, and (s_{0}) is the initial height. the acceleration due to gravity is (- 4.9 m/s^{2}). a rocket is launched from the ground at an initial velocity of 39.2 meters per second. which equation can be used to model the height of the rocket after (t) seconds? (s(t)=-4.9t^{2}+39.2) (s(t)=-4.9t^{2}+39.2t) (s(t)=-4.9t^{2}+39.2t + 39.2) (s(t)=-4.9t^{2}+39.2t-39.2)

Answer

Explanation:

Step1: Identify given values

Given $g=-4.9$ m/s², $v_0 = 39.2$ m/s, and since the rocket is launched from the ground, $s_0=0$.

Step2: Substitute values into formula

Substitute $g$, $v_0$, and $s_0$ into $s(t)=gt^{2}+v_0t + s_0$. We get $s(t)=-4.9t^{2}+39.2t+0=-4.9t^{2}+39.2t$.

Answer:

$s(t)=-4.9t^{2}+39.2t$ (corresponding to the second - option in the multiple - choice list)