Four people are pulling in different directions on a shopping cart. The magnitude of their pulling forces and the directions relative to straight east are indicated below. Jane: 80 pounds, straight east (0 degrees relative to east) Brittany: 100 pounds, north (90 degrees relative to east) Robyn: 80 pounds, southwest (225 degrees relative to east) Scott: 100 pounds, northwest (135 degrees relative to east) Which way with the shopping cart go?

17⁰ north of west

Explanation:

We shall represent forces by vector notations . i will represent unit vector towards east and j will represent unit vector towards north .

Jane: 80 pounds, straight east

F₁ = 80 i

Brittany: 100 pounds, north (90 degrees relative to east)

F₂ = 100 j

Robyn: 80 pounds, southwest (225 degrees relative to east ) or 45⁰ south of west

F₃ = - 80cos 45  i - 80 sin45 j = - 80/√2 x ( i + j )

= - 40√2 ( i + j )

Scott: 100 pounds, northwest (135 degrees relative to east) or 45⁰ west of north .

F₄ = - 100 cos 45 i + 100 sin45 j =  50√2 ( - i + j )

Resultant force

= F₁ + F₂ + F₃ + F₄

F =  80 i + 100 j + - 40√2 ( i + j ) + 50√2 ( - i + j )

F = 80 i - 90√2 i + 110√2 j

80 i - 127.26 i + 114.14 j

F = - 47.26 i + 114.14 j

Direction of force

TanФ = 114.14 / 47.26 = 2.4

Ф = 67⁰

67⁰ north of west .

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.