Questions: Some os vetores. (1 Point) vec(u) e vec(s) 4,8 i+29 j 29 i+4,8 j 29 i-4,8 j -4,8 i+29 j

Solution Steps

Given:

• Magnitude of \( \vec{u} \) is 17
• Angle with the x-axis is 40°

Calculate the components: \[ u_x = 17 \cos(40^\circ) \] \[ u_y = 17 \sin(40^\circ) \]

Using trigonometric values: \[ \cos(40^\circ) \approx 0.766 \] \[ \sin(40^\circ) \approx 0.643 \]

So, \[ u_x = 17 \times 0.766 \approx 13.022 \] \[ u_y = 17 \times 0.643 \approx 10.931 \]

Given:

• Magnitude of \( \vec{s} \) is 20
• Angle with the y-axis is 25°

Calculate the components: \[ s_x = 20 \sin(25^\circ) \] \[ s_y = 20 \cos(25^\circ) \]

Using trigonometric values: \[ \sin(25^\circ) \approx 0.423 \] \[ \cos(25^\circ) \approx 0.906 \]

So, \[ s_x = 20 \times 0.423 \approx 8.46 \] \[ s_y = 20 \times 0.906 \approx 18.12 \]

Add the corresponding components: \[ \vec{u} + \vec{s} = (u_x + s_x) \hat{i} + (u_y + s_y) \hat{j} \]

So, \[ \vec{u} + \vec{s} = (13.022 + 8.46) \hat{i} + (10.931 + 18.12) \hat{j} \] \[ \vec{u} + \vec{s} = 21.482 \hat{i} + 29.051 \hat{j} \]

Final Answer