Aperson pushes a 16.0-kg shopping cart at a constant velocity for a distance of 16.0 m. she pushes in a direction 30.0° below the horizontal. a 54.0-n frictional force opposes the motion of the cart. (a) what is the magnitude of the force that the shopper exerts? n (b) determine the work done by the pushing force. j (c) determine the work done by the frictional force. j (d) determine the work done by the gravitational force. j

Let: 
P - pushing force, 
t - angle below horizontal, 
F -  friction force. 

Resolving horizontally: 
P cos(t) = F 

(a) 
P = F / cos(t) 
= 54  / cos(30.0) 
= 62.35 

(b) 
Work done by P 
= P cos(t) * 16.0 
= F * 16.0 
= 54.0 * 16.0 
= 864J 

(c) 
Work done by F 
= - F * 16.0 
= - 54 * 16.0 
= - 864 J. 

(d) 
As there is no motion vertically, the work done by the gravitational force is 0.

a lot of it means it can be "burned" for energy and sold at one price. if it is scarce, the price will go up

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)