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Justin and Pedro each launched a toy rocket into the air. The height of Justin’s rocket is modeled by the equation h = –16t2 + 60t + 2. Pedro launched his rocket from the same position, but with an initial velocity double that of Justin’s. Which equation best models the height of Pedro’s rocket?

Verified Answer :

the position equatioin is: s(t) = –16t2 + v0t + h0, where v0  represents the initial velocity of the object and h0 represents the initial height of the object . So, since the position function represents the height of an object in t seconds, s(t)= h(t). Therefor, v0= intial velocity= 60t. Double 60t and then replace that answer with 60t from Justin's rocket's equation in order to find Pedro's rocket's equation.

Answer:

Height of justin rocket , h =-\(16 t^2 + 60 t + 2\)

Displacement (h) = Time taken (t) × Velocity (v)

→ h = t v

Velocity of Pedro's rocket is twice of Justin rocket.

It gives , h = 2 t v

Velocity is inversely proportional with time.

So , if in the equation of Height of Justin rocket if we replace t by \(\frac{t}{2}\)  , we can get height of Pedro's rocket.

H = Height of Pedro's rocket

H= -16 (t/2)² + 60 × (t/2) + 2

 = - 4 t² + 30 t + 2

is the equation that models the height of Pedro's rocket.


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