Respuesta :
At the maximum height, the vertical velocity of an object in free fall is zero
The maximum height reached by the rocket, is 7761.6 m
The reason the maximum height is correct;
The given parameters are;
The initial upward acceleration of the rocket, a = 44.1 m/s²
The duration of the initial acceleration, t = 8.00 s
Acceleration due to gravity, g = 9.80 m/s²
Required:
To find the maximum height reached
Solution:
The distance covered with the initial acceleration, h, is given as follows;
[tex]h = u \cdot t + \dfrac{1}{2} \cdot a \cdot t^2[/tex]
Where;
u = The initial velocity
The height reached during the initial acceleration is therefore;
[tex]h = \dfrac{1}{2} \cdot 44.1 \cdot 8^2 = 1,411.2[/tex]
The velocity, v, reached during the initial acceleration is given as follows;
v = u + a·t
∴ v = 44.1×8 = 352.8
The velocity reached during the initial acceleration, v = 352.8 m/s
The time to reach maximum height is given as follows;
v = u + g·t
Where;
u = 352.8
v = 0
t = u/g
∴ t = 352.8/9.80 = 36
The time to reach maximum height, t = 36 seconds
The height reached using u = 352.8, t = 36 seconds gives;
[tex]h = u \cdot t + \dfrac{1}{2} \cdot a \cdot t^2[/tex]
[tex]h = 352.8 \times 36 - \dfrac{1}{2} \times 9.80 \times 36^2 = 6,350.4[/tex]
The maximum height reached, [tex]y_{max}[/tex] by the rocket, is 1411.2 m + 6350.4 m = 7761.6 m
Learn more about free fall motion here:
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