How Much Vertical Acceleration Does a Jet Need to Avoid a Hill?

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KukyZ
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Homework Statement
A jet travels at speeds of 1300 km/h at 35 m above ground level. Suddenly it meets a slope of 10% and immediately corrects its trajectory accelerating upwards (a(t) constant, in the direction of y).
How much should the acceleration be worth to avoid impact with the ground?
Relevant Equations
x=V
y=35+1/2 at^2
The answer should be 10 m/s^2 but I don't know how to solve it
 
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  • #2
I guess you meant x=vt.
So you have the position of the jet at time t. What about the position of the ground below it?
 
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  • #3
KukyZ said:
Homework Statement: A jet travels at speeds of 1300 km/h at 35 m above ground level. Suddenly it meets a slope of 10% and immediately corrects its trajectory accelerating upwards (a(t) constant, in the direction of y).
How much should the acceleration be worth to avoid impact with the ground?
Relevant Equations: x=V
y=35+1/2 at^2

The answer should be 10 m/s^2 but I don't know how to solve it
I suspect that the problem is asking for the smallest possible vertical acceleration that will prevent a collision with the ground. Start by drawing a diagram of the jet's trajectory. The jet must barely graze the hillside.

How do you know that the answer is 10 m/s2?
 
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FAQ: How Much Vertical Acceleration Does a Jet Need to Avoid a Hill?

1. What factors determine the vertical acceleration required for a jet to avoid a hill?

The vertical acceleration required for a jet to avoid a hill depends on several factors, including the jet's current speed, the altitude of the jet, the distance to the hill, the height of the hill, and the jet's climb performance capabilities. Additionally, environmental conditions such as air density and wind speed can also influence the required acceleration.

2. How do you calculate the necessary vertical acceleration for a jet to clear a specific hill?

To calculate the necessary vertical acceleration, you can use the equation a = (V^2 - U^2) / (2 * d), where 'a' is the vertical acceleration, 'V' is the final vertical speed required to clear the hill, 'U' is the initial vertical speed, and 'd' is the vertical distance to be covered. This equation is derived from the kinematic equations of motion.

3. What is the role of the jet's climb rate in avoiding a hill?

The jet's climb rate, which is the vertical speed at which the jet can ascend, plays a crucial role in avoiding a hill. A higher climb rate means the jet can gain altitude more quickly, reducing the required vertical acceleration. The climb rate is influenced by the jet's thrust, weight, and aerodynamic properties.

4. How do pilot response time and decision-making impact the vertical acceleration needed?

Pilot response time and decision-making are critical factors. A delayed response can reduce the available time to initiate the climb, increasing the required vertical acceleration. Quick and accurate decision-making allows the pilot to start the climb sooner, potentially reducing the necessary acceleration to avoid the hill.

5. Can autopilot systems assist in managing the vertical acceleration to avoid obstacles like hills?

Yes, modern autopilot systems can assist in managing vertical acceleration to avoid obstacles. These systems use sensors and terrain databases to detect potential hazards and can automatically adjust the jet's flight path and vertical speed to ensure safe clearance. However, the pilot must still monitor and, if necessary, override the system to ensure safety.

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