A 0.2 kgkg plastic cart and a 20 kgkg lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a distance of 1 mm, starting from rest. After traveling 1 mm, is the momentum of the plastic cart greater than, less than, or equal to the momentum of the lead cart? Match the words in the left column to the appropriate blanks in the sentences on the right.

The rocket sled shown below decelerates at a rate of 196m/s2 . What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is 2.10103kg

If the rocket sled shown in the previous problem starts with only one rocket burning, what is the magnitude of this acceleration? Assume that the mass of the system is 2.10103kg , the thrust Tis 2.40104N , and the force of friction opposing the motion is 650.0 N. (b) Why is the acceleration n one-fourth of what it is with all rockets burning?

between points in a plane do not change when a coordinate system is rotated In other words, the magnitude of a vector Is invariant under rotations of the coordinate system. Suppose a coordinate system S is rotated about its origin by angle to become a new coordinate system S’, as shown in the following figure. A point in a plane has coordinates (x,y)in S and coordinates (x,y) in S’. (a) Show that, during the transformation of rotation, the coordinates in S are expressed in terms of the coordinates in S by the following relations: {x=xcos+ysiny=xsin+ycos (b) Show that the distance of point Pto the origin is invariant under rotations of the coordinate system. Here, you have to show that x2+y2=x2+y2. (c) Show that the distance between points Pand Q is invariant under rotations of the coordinate system. Here, you have to show that ( xP =xQ )2+( yP yQ )2=( xP =xQ )2+( yP yQ )2 .