4. Two ships leave port at the same time. One sails south at 15 mi/h, and the other sails east at 20 mi/h. Find a function that models the distance, D, between the ships in terms of the time, t (in hours), elapsed since their departure.

(D = 25t) is the function that models the distance, D, between the ships in terms of the time, t (in hours), elapsed since their departure.

Explanation:

First ship sailed south at a speed of 15 mi/h, let this be = A

Second ship sailed east at a speed of 20 mi/h, let this be = B

Making a sketch of the position of this two ships, we will obtain a right angled triangle.

The distance between the two ships is the hypotenuse of the right angled triangle,  let this be = D

From Pythagoras theorem

D² = A² + B²

To find a function that models the distance, D, between the ships in terms of the time, t (in hours), elapsed since their departure.

⇒ D² = (At)² + (Bt)²

   D² = (15t)² + (20t)²

   D² = 225t² + 400t²

   D² = 625t²

   D  = √625t²

   D  = 25t

Therefore, (D = 25t) is the function that models the distance, D, between the ships in terms of the time, t (in hours), elapsed since their departure.

gets less

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.