The projectile motion of an object can be modeled using s(t)=gt^2+v0t+s0, where g is the acceleration due to gravity, t is the time in seconds since launch ,s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is -4.9m/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 + Vot + 282.24

Step-by-step explanation:

Since the rocket is launched from the ground, So = 0 and S(t) = 0

Using s(t)=gt^2+v0t+s0 to get time t

Where g acceleration due to gravity = -4.9m/s^2. and

initial velocity = 39.2 m/a

0 = -4.9t2 + 39.2t

4.9t = 39.2

t = 8s

Substitute t in the model equation

S(t) = -49(8^2) + 3.92(8) + So

Let S(t) =0

0 = - 313.6 + 31.36 + So

So = 282.24m

The equation that can be used to model the height of the rocket after t seconds will be:

S(t) = -4.9t^2 + Vot + 282.24

the answer is 175.4379

step-by-step explanation: