Respuesta :
Answer:
h = 1094.69m
The maximum height above the ground the rocket will achieve is 1094.69m.
Explanation:
The maximum height h is;
h = height covered during acceleration plus height covered when the motor stops.
h = h1 + h2 .......1
height covered during acceleration h1 can be derived using the equation of motion;
h1 = ut + 0.5at^2
Initial speed u = 0
h1 = 0.5at^2
acceleration a = 20 m/s^2
Time t = 6.0 s
h1 = 0.5×(20 × 6^2)
h1 = 0.5(20×36)
h1 = 360 m
height covered when the motor stops h2 can be derived using equation of motion;
h2 = ut + 0.5at^2 .......2
Where;
a = g = acceleration due to gravity = -9.8 m/s^2
The speed when the motor stops u;
u = at = 20 m/s^2 × 6.0 s = 120 m/s
Time t2 can be derived from;
v = u - gt
v = 0 (at maximum height velocity is zero)
u = gt
t = u/g
t = 120m/s / 9.8m/s^2
t = 12.24 seconds.
Substituting the values into equation 2;
h2 = 120(12.24) - 0.5(9.8×12.24^2)
h2 = 734.69376 m
h2 = 734.69 m
From equation 1;
h = h1 + h2 . substituting the values;
h = 360m + 734.69m
h = 1094.69m
The maximum height above the ground the rocket will achieve is 1094.69m.
