Answer:
[tex]d(t)=\sqrt{(300+30t)^2+(60t)^2}[/tex]
Step-by-step explanation:
Let t represents the time in hours,
We know that,
[tex]Speed =\frac{Distance}{Time}[/tex]
[tex]\implies Distance = Speed\times time[/tex]
Since, the speed of truck = 30 miles per hour,
So, the distance covered by the truck in t hours = 30t miles,
Similarly,
Speed of car = 60 miles per hour,
So, the distance covered by car in t hours = 60t miles,
∵ Truck is 300 miles east of the car initially,
Thus, the distance of the truck from the starting point = 30t + 300,
While the distance of the car from the starting point = 60 t,
Now, these two vehicles are going in the directions which are at right angled ( car is going north and truck is going west )
Using the Pythagoras theorem,
Distance between them after t hours,
[tex]d(t)=\sqrt{(300+30t)^2+(60t)^2}[/tex]
Which is the required function.
