An aeroplane is heading north at a speed of 300km/h . If wind begins blowing at a speed of 50km/h from the west , calculate the magnitude of the velocity of the aeroplane relative to ground?
sqrt (300^2 + 50^2)
R^2= y^2+ x^2
R^2=300^2+50^2
R^2=90,000+2,500
R^2=√92,500
R=304.14km/h
Thanks so much
To calculate the magnitude of the velocity of the airplane relative to the ground, we need to use vector addition.
First, we need to break down the velocity of the airplane into its north and west components. Since the airplane is heading north at 300 km/h, its north component of velocity is 300 km/h.
Since the wind is blowing from the west at 50 km/h, its west component of velocity is 50 km/h.
To find the resultant velocity, we can use the Pythagorean theorem. The magnitude of the resultant velocity can be found using the formula:
Resultant velocity = sqrt((north velocity)^2 + (west velocity)^2)
Plugging in the values:
Resultant velocity = sqrt((300 km/h)^2 + (50 km/h)^2)
= sqrt(90000 km^2/h^2 + 2500 km^2/h^2)
= sqrt(92500 km^2/h^2)
= 304.13 km/h (approximately)
Therefore, the magnitude of the velocity of the airplane relative to the ground is approximately 304.13 km/h.