Answer with Explanation:
We are given that
Velocity,v=24 m/s west
Acceleration,a=[tex]2.5m/s^2[/tex]
[tex]\theta=53^{\circ}[/tex](N of W)
Horizontal component of acceleration=Tangential acceleration
Tangential acceleration,[tex]a_x=acos\theta=2.5cos53=1.505 m/s^2[/tex]
Radial acceleration=Vertical acceleration=[tex]a_y=asin\theta[/tex]
[tex]a_y=2.5sin53=1.998 m/s^2[/tex]
Radial acceleration,[tex]a_y=\frac{v^2}{R}[/tex]
[tex]1.998=\frac{(24)^2}{R}[/tex]
[tex]R=\frac{(24)^2}{1.998}[/tex]
[tex]R=288.29 m[/tex]
Time,[tex]t=\frac{2\pi R}{velocity}[/tex]
[tex]t=\frac{2\pi(288.29)}{24}[/tex]
[tex]t=75.47 s[/tex]
