To find the magnitude and direction angle for u + v, we can use the following formulas:
Magnitude of u + v = √((magnitude of u)^2 + (magnitude of v)^2 + 2(magnitude of u)(magnitude of v)cos(θv - θu))
Direction angle for u + v = θu + arccos((magnitude of u + magnitude of v)cos(θu - θv)/(magnitude of u + magnitude of v))
Plugging in the given values:
Magnitude of u = 15
Magnitude of v = 18
θu = 35°
θv = 60°
Magnitude of u + v = √((15)^2 + (18)^2 + 2(15)(18)cos(60°-35°))
= √(225 + 324 + 540cos(25°))
≈ √(549 + 540(0.9063))
≈ √(549 + 490.18)
≈ √1039.18
≈ 32.2 (rounded to the nearest tenth)
Direction angle for u + v = 35° + arccos((15 + 18)cos(35° - 60°)/(15 + 18))
= 35° + arccos(33cos(-25°)/33)
= 35° + arccos(cos(-25°))
≈ 35° + (-25°)
≈ 10° (rounded to the nearest whole degree)
Therefore, the magnitude of u + v is approximately 32.2 and the direction angle is approximately 10°.
Magnitude of u = 15, direction angle θ = 35°
Magnitude of v = 18, direction angle θ = 60°
Find the magnitude and direction angle for u + v.
Round the magnitude to the nearest tenth and the direction angle to the nearest whole degree.
1 answer