The hypersonic aeroplane will have jet engines and a rocket engine.The speed of aeroplanes can be measured on a uniform scale called the Mach scale.Mach 1 = 330 m/sThe jet engines will accelerate the aeroplane to Mach 5.5.The rocket engine will accelerate the aeroplane from Mach 5.5 to Mach 25.5 in 300 s.The average resultant force on the aeroplane when the rocket engine is usedwill be 630 000 N.Calculate the mass of the hypersonic aeroplane.Give your answer to 2 significant figures

To calculate the mass of the hypersonic aeroplane, we first need to find the acceleration of the aeroplane when the rocket engine is used.

1. First, we need to convert the Mach speeds to m/s. We know that Mach 1 = 330 m/s. So, Mach 5.5 = 5.5 * 330 m/s = 1815 m/s and Mach 25.5 = 25.5 * 330 m/s = 8415 m/s.

2. The change in speed (final speed - initial speed) when the rocket engine is used is 8415 m/s - 1815 m/s = 6600 m/s.

3. The time taken for this change in speed is given as 300 s. So, the acceleration (change in speed/time) is 6600 m/s / 300 s = 22 m/s².

4. Now, we can use Newton's second law of motion, which states that force = mass * acceleration, to find the mass of the aeroplane. Rearranging this equation gives us mass = force / acceleration.

5. Substituting the given force (630,000 N) and the calculated acceleration (22 m/s²) into this equation gives us mass = 630,000 N / 22 m/s² = 28636.36 kg.

6. To 2 significant figures, the mass of the hypersonic aeroplane is 29000 kg.