A jet fighter with mass 5000 kg accelerates from 360 km/hr in 10b s. Compute the minimum thrust required by the jet's engines.
To compute the minimum thrust required by the jet's engines, we need to first determine the change in velocity (Δv) of the jet.
1. Convert the initial velocity from km/hr to m/s:
360 km/hr = 360,000 m/3600 s = 100 m/s
2. Calculate the final velocity using the formula: vf = vi + at
Assuming the jet starts from rest (vi = 0) and accelerates uniformly, we can find vf:
vf = 0 + (a)(10 s), where a is the acceleration.
3. Calculate the acceleration using the formula: a = Δv / t
Δv = vf - vi = vf - 0 = vf
a = vf / t
Now, let's find the acceleration:
a = Δv / t = vf / t
vf = (100 m/s) + a(10 s)
4. Rearrange the equation to solve for a:
vf = 100 m/s + 10a
100 m/s + 10a = vf
5. Substitute the given final velocity:
100 m/s + 10a = vf = (5000 kg) * vf / 5000 kg
6. Solve for 'a':
100 m/s = (5000 kg) * vf / 5000 kg - 10a
7. Multiply by 5000 kg:
100 m/s * 5000 kg = (5000 kg) * vf - 50000 * a
500000 kg·m/s = 5000 kg·vf - 50000 kg·m/s^2
8. Rearrange the equation and isolate 'a' to find the minimum acceleration:
50000 kg·m/s^2 = 5000 kg·vf
a = (50000 kg·m/s^2) / (5000 kg)
a = 10 m/s^2
Now that we have the acceleration 'a', we can calculate the minimum thrust required by the jet's engines.
9. Use Newton's second law: F = ma
F = (5000 kg) * (10 m/s^2)
F = 50000 N
Therefore, the minimum thrust required by the jet's engines is 50,000 Newtons (N).