Answer:
81.8 m/s
Explanation:
The initial velocity of the plane is:
[tex]v_0=115 m/s[/tex] (toward east)
So, decomposing along the x- and y- directions:
[tex]v_{x0} = 115 m/s\\v_{y0} = 0[/tex]
(we took east as positive x-direction and north as positive y-direction)
The acceleration is
[tex]a=2.88 m/s^2[/tex] (northwest, so the angle with the positive x-direction is 135 degrees)
Decomposing it along the two directions:
[tex]a_x = a cos 135^{\circ} = (2.88 m/s^2)(cos 135^{\circ})=-2.04 m/s^2\\a_y = a sin 135^{\circ} = (2.88 m/s^2)(sin 135^{\circ})=2.04 m/s^2[/tex]
So the two components of the velocity after a time t = 25.0 s will be
[tex]v_x = v_{x0} + a_x t = 115 m/s + (-2.04 m/s^2)(25.0 s)=64 m/s\\v_y = v_{y0} + a_y t = 0 m/s + (2.04 m/s^2)(25.0 s)=51 m/s[/tex]
So, the magnitude of the velocity of the plane will be
[tex]v=\sqrt[v_x^2+v_y^2}=\sqrt{(64 m/s)^2+(51 m/s)^2}=81.8 m/s[/tex]
