Answer:
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
