Benny wonders why when he presses his finger against a map nothing happens to the map. However if he presses a thumbtack into the map using the same force the tack will probably poke a hole in the map.

The pressure exerted on a surface by an object increases as the surface area of contact decreases.

Explanation:

Pressure measures the amount of force exerted per a given area of an object. From this definition, the surface area of the object and force applied, affects the pressure applied.

As Benny presses his finger against a map, nothing happens to the map because the force applied is affected by the increased surface area of his finger. However as he presses a thumbtack into the map using the same force the tack will probably poke a hole in the map because the small( decreased) surface area of the sharp point of the thumbtack produces a much larger pressure on the map than the area of Benny finger. I hope this helps, thanks!

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west