A person walks in the following pattern: 3.0 km north, then 2.4 km west, and finally 5.0 km south. (a) How far and (b) at what angle (measured counterclockwise from east) would a bird fly in a straight line from the same starting point to the same final point?

3.12 km

320.19°

Explanation:

From the diagram, the starting point is O.

The resultant is line OC.

Hence, using Pythagoras Theorem, we have that:

OC² = OE² + EC²

OC² = 2.4² + 2²

OC² = 5.76 + 4

OC² = 9.76

OC = 3.12 km

The angle, θ, will be:

tanθ = (2/2.4)

tanθ = 0.833

θ = 39.81°

Measuring counterclockwise from the East, the angle will be 360 - 39.81 = 320.19°.

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.