Podcast
Questions and Answers
What is the take off speed of the jet in km/hr?
What is the take off speed of the jet in km/hr?
278 km/hr
What is the distance over which the catapult accelerates the jet in metres?
What is the distance over which the catapult accelerates the jet in metres?
94 metres
What is the formula that relates speed, acceleration, and time?
What is the formula that relates speed, acceleration, and time?
v = at
What is the formula for distance covered with constant acceleration?
What is the formula for distance covered with constant acceleration?
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If the jet's take off speed is 278 km/hr, what is the speed in metres per second?
If the jet's take off speed is 278 km/hr, what is the speed in metres per second?
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How do you calculate the time taken for the fighter to be accelerated to take off speed?
How do you calculate the time taken for the fighter to be accelerated to take off speed?
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Study Notes
Aircraft Carrier Catapult Acceleration Calculation
- Acceleration can be calculated using the final speed and distance available for the jet to reach takeoff speed.
- Given take-off speed: 278 km/hr; convert to m/s for calculations (1 km/hr = 1/3.6 m/s).
- Conversion: 278 km/hr = 278 / 3.6 ≈ 77.22 m/s.
Distance and acceleration
- Distance over which the catapult accelerates the jet: 94 m.
- Use the formula ( S = \frac{1}{2} a t^2 ) rearranged gives acceleration ( a = \frac{2S}{t^2} ).
- To find time ( t ), use ( v = at ) which can be rewritten as ( t = \frac{v}{a} ).
Acceleration Calculation
- When acceleration is constant: combine both equations to eliminate the variable ( t ).
- Substitute ( t ) from the second equation into the first, leading to ( S = \frac{v^2}{2a} ), allowing the calculation of acceleration ( a = \frac{v^2}{2S} ).
- Calculating:
- ( a = \frac{(77.22)^2}{2 \times 94} ).
- Resulting in ( a ≈ 36.87 , \text{m/s}^2 ).
Time Calculation
- After finding acceleration, calculate time:
- Substitute back to find ( t ) using ( t = \frac{v}{a} ).
- ( t = \frac{77.22}{36.87} ).
- Resulting in ( t ≈ 2.09 , \text{seconds} ).
Summary
- Final acceleration of the jet is approximately 36.87 m/s².
- Time taken for the jet to reach take-off speed is approximately 2.09 seconds.
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Description
This quiz covers the calculations involved in determining the acceleration of a jet using an aircraft carrier catapult. You'll learn to convert speeds, use kinematic equations, and calculate both acceleration and time. Test your knowledge on the physics behind jet take-off dynamics.
