The compass of an airplane indicates that it is headed due north and its airspeed indicator shows that it is moving through the
air at 240 km/hr. If there is a wind of 100 km/hr from west to east. (Hint: in this problem there is no need to convert to m/s)
a) Draw an appropriate diagram and determine the velocity of the plane relative to the earth?
b) What direction should the pilot head to travel due north and what then will be her velocity relative to the earth?
a) Draw an appropriate diagram and determine the velocity of the plane relative to the earth?
b) What direction should the pilot head to travel due north and what then will be her velocity relative to the earth?
1 answer:
Answer:
Airplane speed relative to the ground is 260 km/h and θ = 22.6º direction from north to east
Explanation:
This is a problem of vector composition, a very practical method is to decompose the vectors with respect to an xy reference system, perform the sum of each component and then with the Pythagorean theorem and trigonometry find the result.
Let's take the north direction with the Y axis and the east direction as the X axis
Vy = 240 km / h airplane
Vx = 100 Km / h wind
a) See the annex
Analytical calculation of the magnitude of the speed and direction of the aircraft
V² = Vx² + Vy²
V = √ (240² + 100²)
V = 260 km/h
Airplane speed relative to the ground is 260 km/h
Tan θ = Vy / Vx
tan θ = 100/240
θ = 22.6º
Direction from north to eastb
b) What direction should the pilot have so that the resulting northbound
Vo = 240 km/h airplane
Vox = Vo cos θ
Voy = Vo sin θ
Vx = 100 km / h wind
To travel north the speeds the x axis (East) must add zero
Vx -Vox = 0
Vx = Vox = Vo cos θ
100 = 240 cos θ
θ = cos⁻¹ (100/240)
θ = 65.7º
North to West Direction
The speed in that case would be
V² = Vx² + Vy²
To go north we must find Vy
Vy² = V² - Vx²
Vy = √( 240² - 100²)
Vy = 218.2 km / h
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Answer:
Velocity= 19.05 m/s
Kinetic energy= 3.08 J
Explanation:
The corn possess potential energy. Feom law of conservation of energy, all the potential eneegy will be converted to kinetic energy, with negligible friction.
Potential energy, PE= kinetic energy, KE
Potential energy is given by mgh while kinetic energy is given by
Equating
Making v the subject of the formula then
Substituting 9.81 m/s2 for g and 18.5 m for h then the velocity will be
To get the kinetic eneegy, since PE=KE AND KE is
Substituting v with 19.05 and m with 0.017 kg we have
This can also be achieved by mgh since PE=KE hence 0.17*9.81*18.5=3.085245 J and the results are slightly different due to small energy losses and rounding off of values.