One of the world's fastest helicopters, the Westland Lynx, has a top speed of
4.00 × 102 km/h. If its kinetic energy at this speed is 2.10 x 10' I, what is the helicopter's mass?
The kinetic energy (KE) of an object is given by the equation:
KE = (1/2) * m * v^2
where m is the mass of the object and v is its velocity. Rearranging the equation to solve for mass (m), we have:
m = 2 * KE / v^2
Plugging in the given values, we get:
m = 2 * (2.10 x 10^11 J) / (4.00 x 10^2 km/h)^2
We need to convert the speed, which is given in km/h, to m/s. There are 1000 meters in a kilometer and 3600 seconds in an hour, so:
(m/s) = (km/h) * (1000 m/km) / (3600 s/h)
Plugging in the given value, we get:
v = (4.00 x 10^2 km/h) * (1000 m/km) / (3600 s/h)
v ≈ 111.11 m/s
Now, plugging in the values for KE and v:
m = 2 * (2.10 x 10^11 J) / (111.11 m/s)^2
Calculating this expression gives:
m = 3.10 x 10^6 kg
Therefore, the helicopter's mass is approximately 3.10 x 10^6 kg.