Aeroplane takes off from Mumbai to Delhi with velocity 50 kilometre per hour in north east direction
a wind is blowing at 25 kilometre per hour what is the resultant displacement of aeroplane in 2 hours
50root3/2i^-(-50/2j^)=velocity of aeroplane with respect of wind
Vaeroplane=50root3/2 Vwind=-50/2
displacement=25root3*2hrs=86.2km
To find the resultant displacement of the aeroplane, we need to calculate the vector sum of the velocity of the aeroplane and the wind.
Given:
Velocity of the aeroplane = 50 km/h (in the northeast direction)
Velocity of the wind = 25 km/h
Since the aeroplane is flying in the northeast direction, we can consider its velocity as a diagonal vector with components in the east and north directions. The magnitude of the eastward component is given by:
Eastward component = velocity of the aeroplane × cos(45°)
= 50 km/h × cos(45°) [since northeast is 45° from the east direction]
Similarly, the magnitude of the northward component is given by:
Northward component = velocity of the aeroplane × sin(45°)
= 50 km/h × sin(45°)
Now, let's calculate the magnitude and direction of the resultant displacement.
Since we are given the velocities in km/h, we can directly multiply the components by the time (2 hours) to find the displacement.
Magnitude of the resultant displacement = [(Eastward component × 2 hours)^2 + (Northward component × 2 hours)^2]^(1/2)
Direction of the resultant displacement = arctan(Northward component × 2 hours / Eastward component × 2 hours)
Let's calculate:
Eastward component = 50 km/h × cos(45°) = 50 × (√2/2) = 50√2/2 = 25√2 km/h
Northward component = 50 km/h × sin(45°) = 50 × (√2/2) = 50√2/2 = 25√2 km/h
Magnitude of the resultant displacement = [(25√2 km/h × 2 hours)^2 + (25√2 km/h × 2 hours)^2]^(1/2)
= [(50√2 km)^2 + (50√2 km)^2]^(1/2)
= [2500 km^2 + 2500 km^2]^(1/2)
= [5000 km^2]^(1/2)
= √5000 km
= 70.71 km (approx)
Direction of the resultant displacement = arctan(25√2 km/h × 2 hours / 25√2 km/h × 2 hours)
= arctan(1)
= 45°
Therefore, the resultant displacement of the aeroplane in 2 hours is approximately 70.71 km in the northeast direction.
To find the resultant displacement of the airplane in 2 hours, we need to consider both the velocity of the airplane and the effect of the wind.
Given:
- Velocity of the airplane: 50 km/h in the northeast direction
- Wind velocity: 25 km/h
First, let's resolve the airplane's velocity into its north and east components. Since the airplane is moving in a northeast direction, we can determine the north and east components using trigonometry.
The northeast direction can be broken down into two perpendicular components: north and east.
Let's assume that the angle formed between the velocity vector and the north direction is 45 degrees. This assumption allows us to simplify the trigonometric calculations.
To find the north component (Vn) of the velocity:
Vn = Velocity * cos(angle)
Vn = 50 km/h * cos(45 degrees)
Vn = 50 km/h * (√2/2)
Vn = 25√2 km/h
To find the east component (Ve) of the velocity:
Ve = Velocity * sin(angle)
Ve = 50 km/h * sin(45 degrees)
Ve = 50 km/h * (√2/2)
Ve = 25√2 km/h
Now, let's consider the effect of the wind on the airplane's motion. The wind is blowing at a velocity of 25 km/h.
To calculate the resultant displacement, we need to add the displacements caused by the airplane's velocity and the wind.
The north component displacement (Dn) caused by the airplane's velocity is given by:
Dn = Vn * t,
where t is the time (2 hours).
Dn = 25√2 km/h * 2 hours
Dn = 50√2 km
The east component displacement (De) caused by the airplane's velocity is given by:
De = Ve * t,
where t is the time (2 hours).
De = 25√2 km/h * 2 hours
De = 50√2 km
Now, let's find the displacement caused by the wind.
The wind is blowing in a direction perpendicular to the airplane's velocity, so it does not affect the north and east components of the displacement.
The displacement caused by the wind is given by:
Dw = Wind Velocity * t,
where t is the time (2 hours).
Dw = 25 km/h * 2 hours
Dw = 50 km
To find the resultant displacement (Dr), we need to add the north and east components of the displacement caused by the airplane's velocity and the displacement caused by the wind.
Dr = √(Dn^2 + De^2 + Dw^2)
Dr = √((50√2)^2 + (50√2)^2 + (50)^2)
Dr = √(5000 + 5000 + 2500)
Dr = √12500
Dr ≈ 111.8 km
Therefore, the resultant displacement of the airplane in 2 hours is approximately 111.8 km.
add the following vectors:
a) 50@45
b) 25@?????
you have to have direction of wind....