A pilot direct his plane north and the plane's velocity in still air is 245km/hr. If there is a strong wind of 105km/hr blowing west, what is the ground velocity of the plane?
v=sqrt{(pl)²+v(wind)²} = ...
α= arctan{ w(pl)/v(wind)}=...
north of west
What does sqr and arctan means
sqrt =square root,
arctan = tan⁻¹
- inverse trigonometric function –
To find the ground velocity of the plane, we need to determine the resultant velocity by considering the vectors of the plane's velocity in still air and the velocity of the wind.
Let's break down the velocities into their northward and westward components:
1. The velocity of the plane in still air, 245 km/hr, is directed north. So, its northward component is 245 km/hr, and its westward component is 0 km/hr since it is not moving in that direction.
2. The wind is blowing west at a velocity of 105 km/hr. So, its northward component is 0 km/hr since it is not moving northward, and its westward component is -105 km/hr (negative because it is directed opposite to the positive west direction).
Now, we need to calculate the resultant vectors by adding the respective components:
Northward component: 245 km/hr + 0 km/hr = 245 km/hr
Westward component: 0 km/hr + (-105 km/hr) = -105 km/hr
The resultant velocity is a vector with a northward component of 245 km/hr and a westward component of -105 km/hr. To find the magnitude of the resultant velocity, we can use the Pythagorean theorem:
Resultant velocity = √(Northward component^2 + Westward component^2)
= √(245^2 + (-105)^2)
= √(60025 + 11025)
= √(71050)
≈ 266.75 km/hr
So, the ground velocity of the plane, taking into account the wind, is approximately 266.75 km/hr.