Answer:
The distance 5 miles North-East of the intersection between the car and the truck increasing at 71.06 miles per hour at that moment.
Step-by-step explanation:
Looking at the attached figures, Fig 1 shows the diagram of the car and the truck.
Using Pythagoras theorem on Fig 1a,
[tex]l^{2} = \sqrt{3^{2} + 4^{2} }[/tex]
[tex]l = \sqrt{9 +16} \\\\l= \sqrt{25} \\\\l = 5 miles[/tex]
The resultant displacement between the car and the truck at that same moment is 5 miles.
From the velocity vector diagram on Fig 2,
The resultant velocity R is given as
[tex]R = \sqrt{45^{2} + 55^{2} }\\\\R = \sqrt{2025 + 3025 }\\\\R = \sqrt{5050 }\\\\R = 71.06mph[/tex]
Therefore, the distance 5 miles North-East of the intersection between the car and the truck increasing at 71.06 miles per hour at that moment.
