At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Answer:
v = 10.09 m / s, 8.78 North of East
Explanation:
The easiest way to solve this exercise is to decompose the velocities into a coordinate system, where the x-axis coincides with the West-East direction and the y-axis coincides with the South-North direction.
athlete's velocity v₁ₓ = 3 m / s
wind speed 2 v₂ = 10 m / s with direction 65 north of east
sin 65 = v_{2y} / v₂
cos 65 = v₂ₓ / v₂
v_{2y} = v₂ sin 65
v₂ₓ = v₂ cos 65
v_{2y} = 10 sin 65 = 9.06 m / s
v₂ₓ = 10 cos 65 = 4.23 m / s
wind speed 3 v₃ = 8 m / s with direction 70 south of east
This angle measured from the positive side of the x-axis is
θ = 360 - 70
θ = 290
sin 290 = v_{3y} / v₃
cos 290 = v₃ₓ / v₃
v_{3y} = v₃ sin 290
v₃ₓ = v₃ cos 290
v_{3y} = 8 sin 290 = -7.52 m / s
v₃ₓ = 8 cos 290 = 2.74 m / s
now we can find each component of the velocity
X axis
vₓ = v₁ + v₂ₓ + v₃ₓ
vₓ = 3 + 4.23 + 2.74
vₓ = 9.97 m / s
Y axis
v_y = v_{2y} + v_{3y}
v_y = 9.06 - 7.52
v_y = 1.54 m / s
to find the modulus let's use the Pythagorean theorem
v = [tex]\sqrt{v_x^2 + v_y^2 }[/tex]
v = [tex]\sqrt{9.97^2 + 1.54^2}[/tex]
v = 10.09 m / s
let's use trigonometry for the direction
tan θ = v_y / vₓ
θ = tan⁻¹ v_y / vₓ
θ = tan-1 1.54 / 9/97
θ = 8.78
the address is 8.78 North of East
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.