Question

Estimate the kinetic energy (in GJ) of a 98,000 metric ton aircraft carrier moving at a speed of at 32 knots. You will need to look up the definition of a nautical mile to use in converting the unit for speed, where 1 knot equals 1 nautical mile per hour.

Answer 1

Answer:

K = 13.276 GJ

Explanation:

Given:

Mass of the aircraft (m) = 98,000 metric ton

Speed of the aircraft (v) = 32 knots

Kinetic energy of the aircraft (K) = ?

We know that,

1 metric ton = 1000 kg

∴ 98,000 metric ton = 98,000 × 1000 = 9.8 × 10⁷ kg

Also, 1 knot = 1 nautical mile per hour

So, 32 knots = 32 nautical miles per hour

Converting nautical miles per hour to meter per second using the following conversions, we get:

1 nautical mile = 1852 m

1 hour = 3600 s

Therefore, 1 nautical mile per hour = $\frac{1852}{3600}\ m/s$

So, 32 nautical miles per hour = $32\times \frac{1852}{3600}=16.46\ m/s$

Therefore, the mass and speed of the aircraft are:

$m=9.8\times 10^{7}\ kg\\v=16.46\ m/s$

Now, kinetic energy is given as:

$K=\frac{1}{2}mv^2$

Plug in the above values and solve for 'K'. This gives,

$K=\frac{1}{2}\times 9.8\times 10^7\times (16.46)^2\\\\K=4.9\times 270.9316\times 10^7\ J\\\\K=13.276\times 10^2\times 10^7\ J\\\\K=13.276\times 10^9\ J$

Now, we know that, 1 GJ = 10⁹ J

Therefore, the value of 'K' in terms of GJ is given as:

K = 13.276 GJ