Answer:
The magnitude of the truck's velocity relative to the ground is 35.82 m/s.
Explanation:
Given that,
Velocity of car relative to ground = 15.3 m/s
Velocity of truck relative to car = 22.5 m/s
We need to calculate the magnitude of the truck's velocity relative to the ground
We need to calculate the x component of the velocity
[tex]v_{x}=22.5\cos\theta[/tex]
[tex]v_{x}=22.5\cos52^{\circ}[/tex]
[tex]v_{x}=13.852\ m/s[/tex]
We need to calculate the y component of the velocity
[tex]v_{y}=15.3+22.5\sin\theta[/tex]
[tex]v_{y}=15.3+22.5\sin52^{\circ}[/tex]
[tex]v_{y}=33.030\ m/s[/tex]
Using Pythagorean theorem
[tex]|v|=\sqrt{v_{x}^2+v_{y}^2}[/tex]
[tex]|v|=\sqrt{(13.852)^2+(33.030)^2}[/tex]
[tex]|v|=35.82\ m/s[/tex]
Hence, The magnitude of the truck's velocity relative to the ground is 35.82 m/s.