find the altitude change of a 10000-kg fighter which clims and in so doing, loses 100 m/s of airspeed
If we are supposed to assume that the gain in potential energy is equal to the loss in kinetic energy then:
m g h = (1/2)m (V1^2-V2^2)
which is approximately
g h = (1/2)(V1+V2)(V1-V2)
if V is much greater than 100m/s then V1+V2 is about 2 V where V is the starting speed
so
g h = (1/2)(2 V)(100)
h = (100 V/9.81)
so of course I need V
The gain in PE equals the loss of KE only if there is no thrust. That is no way to fly a fighter jet, unless it is doing a zero-g maneuver.
To find the altitude change of a fighter jet, we need to use the principle of conservation of energy.
The potential energy (PE) of an object at a certain height is given by the formula:
PE = m * g * h
where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
When the fighter jet climbs, it loses 100 m/s of airspeed. Let's assume that this change in airspeed is solely converted into potential energy, and neglect other factors like air resistance.
First, we need to calculate the initial kinetic energy (KE) of the fighter jet:
KE = 0.5 * m * v^2
where m is the mass of the fighter jet and v is the initial velocity.
Since the fighter jet loses 100 m/s of airspeed, the initial velocity (v) is reduced by 100 m/s.
Next, we calculate the final kinetic energy (KE') of the fighter jet after it loses airspeed:
KE' = 0.5 * m * (v - 100)^2
Now, we can equate the initial and final kinetic energies with the potential energy:
KE + PE = KE' + PE'
Since the potential energy on both sides of the equation is the same (since we are only considering the change in altitude), we can set up the equation:
0.5 * m * v^2 + PE = 0.5 * m * (v - 100)^2 + PE
Simplifying the equation:
0.5 * m * v^2 = 0.5 * m * (v - 100)^2
Divide both sides of the equation by 0.5 * m:
v^2 = (v - 100)^2
Take the square root of both sides to solve for v:
v = v - 100
100 = 0
This equation does not yield a valid result, which means that it is not possible to determine the altitude change of the fighter jet based solely on the given information.