Question

A truck is 300 miles east of a car and is traveling west at the constant speed of 30 miles/hr meanwhile the car is going north at a constant speed of 60 miles/hr. Express the distance between the car and the truck as a function of time

Answer 1

Answer:

$d(t)=\sqrt{(300+30t)^2+(60t)^2}$

Step-by-step explanation:

Let t represents the time in hours,

We know that,

$Speed =\frac{Distance}{Time}$

$\implies Distance = Speed\times time$

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,

$d(t)=\sqrt{(300+30t)^2+(60t)^2}$

Which is the required function.