Respuesta :
Answer:
The maximum altitude reached with respect to the ground = 0.5 + 0.510 = 1.01 km
Explanation:
Using the equations of motion,
When the rocket is fired from the ground,
u = initial velocity = 0 m/s (since it was initially at rest)
a = 10 m/s²
The engine cuts off at y = 0.5 km = 500 m
The velocity at that point = v
v² = u² + 2ay
v² = 0² + 2(10)(500) = 10000
v = 100 m/s
The velocity at this point is the initial velocity for the next phase of the motion
u = 100 m/s
v = final velocity = 0 m/s (at maximum height, velocity = 0)
y = vertical distance travelled after the engine shuts off beyond 0.5 km = ?
g = acceleration due to gravity = - 9.8 m/s²
v² = u² + 2gy
0 = 100² + 2(-9.8)(y)
- 19.6 y = - 10000
y = 510.2 m = 0.510 km
So, the maximum altitude reached with respect to the ground = 0.5 + 0.510 = 1.01 km
Hope this helps!!!
The maximum altitude this rocket achieves is 1.010 kilometers.
Given the following data:
- Initial speed = 0 m/s (since it accelerated from rest).
- Acceleration = 10 [tex]m/s^2[/tex]
- Altitude = 0.50 km to m = 500 meters.
To calculate the maximum altitude this rocket achieves:
The third equation of motion.
We would calculate the final velocity of this rocket after its engine cut-off at an altitude of 500 meters by using the third equation of motion.
Mathematically, the third equation of motion is given by this formula;
[tex]V^2 = U^2 + 2aS\\\\V^2 = 0^2 + 2\times 10 \times 500\\\\V=\sqrt{10000}[/tex]
V = 100 m/s.
Note: For the next phase of motion, the rocket's final velocity becomes its initial velocity and its final velocity is equal to zero (0) at the maximum altitude.
[tex]0^2 = 100^2 - 2\times 9.8 \times S\\\\19.6S=10000\\\\S=\frac{10000}{19.6}[/tex]
S = 510.20 meters.
In kilometers:
S = 0.510 kilometers.
For the maximum altitude:
Maximum altitude = [tex]0.50 + 0.510[/tex]
Maximum altitude = 1.010 kilometers.
Read more on acceleration here: https://brainly.com/question/24728358
