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?

Question

Mathematics

Graham Jacobs

31 July, 07:56

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?

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Answers (1)

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Autumn Ewing · Answer 1

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