A model rocket is launched from the ground. It starts from rest and accelerates upward at 15.0 m/s2 for 3.00 s. Disregard gravity. What is the V2? b. Then, it has a downward acceleration of -10.0 m/s2 until it reaches its highest point. What is the highest above the ground that the rocket gets? c. What is the TOTAL time in the air?

The final velocity v₂ is 45 m/s

The highest point reached by the rocket is 101.25 m

The total time spent in air by the rocket is 7.5 s

Explanation:

Given;

initial velocity of the rocket, v₁ = 0

final velocity of the rocket, v₂ = ?

upward acceleration of the rocket, a = 15 m/s²

time of acceleration, t = 3 s

The final velocity is given by;

v₂ = v₁ + at

v₂ = 0 + (15 x 3)

v₂ = 45 m/s

The highest point reached by the rocket is given by;

v² = u² + 2ah

where;

u is the initial velocity of rocket when it started decelerating.

thus, u = v₂

v is the final velocity of the rocket at its highest point = 0

0 = v₂² + 2ah

0 = (45)² + (2 x -10 )h

0 = 2025 - 20h

20h = 2025

h = 2025 / 20

h = 101.25 m

Time taken for the rocket to reach its highest point is given by;

h = ut + ¹/₂at²

101.25 = 45t + ¹/₂(-10)t²

101.25 = 45t - 5t²

5t² - 45t + 101.25 = 0

t² - 9t + 20.25 = 0

t = 4.5 s

The total time spent in air by the rocket is given by;

T = upward time + downward time

T = 3 s + 4.5 s

T = 7.5 s

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