Please help me with this physics problem!?

2018-07-09 11:37 am
A plane is flying east at 115 m/s. The wind accelerates it at 2.88 m/s^2 directly northwest. After 25.0 s, what is the magnitude of the velocity of the plane?

回答 (3)

2018-07-09 11:52 am
Formula used, v = vₒ + at

Along the east-west direction (pointing east as positive) :
Initial velocity, vₒ = 115 m/s
Acceleration, a = -2.88 cos45° m/s²
Time taken, t = 25.0 s
Component of final velocity along east-west direction, v = 115 + (-2.88 cos45°) × 25.0 = 64.1 m/s

Along the north-south direction (pointing north as positive) :
Initial velocity, vₒ = 0 m/s
Acceleration, a = 2.88 sin45° m/s²
Time taken, t = 25 s
Component of final velocity along north-south direction, v = 0 + (2.88 cos45°) × 25.0 = 50.9 m/s

Magnitude of final velocity = √(64.1² + 50.9²) = 81.9 m/s
2018-07-09 1:17 pm
ΔVw = a*t = 2.88/√2*25 = 2.88/√2*100/4 = 50.91 m/sec
ΔVn = a*t = 2.88/√2*25 = 2.88/√2*100/4 = 50.91 m/sec
V = √ΔVn^2+(Ve-ΔVw)^2 = √50.91^2+(115-50,91)^2 = 81.85 m/sec
or by applying F.Viete Theorem (aka cosine theorem):
V = √115^2+72^2-2*72*115*cos45° = 81.85 m/sec

heading = arctan (ΔVn/(-ΔVw +Ve) = arctan (50.91/(-50.91+115)) = 38.46° North of East
2018-07-09 11:40 am
idk


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