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Please explain in details how to get the answers for problems below.

Problem 1:
A box is sliding down a plane inclined at an angle of 20 degrees from the horizontal. Find the acceleration of the box, neglecting friction and air resistance.

Possible answers:
(1) 0.342 m^2g
(2) 0.342 m
(3) 0.342 g
(4) 0.342 mg
(5) 0.940 m^2g
(6) 0.940 m
(7) 0.940 g
(8) 0.940 mg

Problem 2:
A box that is hurled up the inclined plane of the above Problem 1, starts up the plane with an initial velocity of 1,000 cm/sec. Find the speed of the box moving up the plane 3 sec later.

Possible answers:
(1) 0 cm/sec
(2) -5.5 cm/sec
(3) 8.9 cm/sec
(4) 10.1 cm/sec
(5) 42.5 cm/sec
(6) 63.3 cm/sec
(7) 75.3 cm/sec
(8) 98.1 cm/sec.

Solution Preview

For the first question, you must first draw a free body diagram very similar to this one:

http://physics.bu.edu/~duffy/semester1/c5_incline.html

The force which moves the box, in that diagram, is mgx. This force can be represented via trigonomic relationships with the force of gravity (mg) itself:

sin theta = mgx / mg

In our case, our ...

Solution Summary

The solution finds the acceleration of the box, neglecting friction and air resistance. It also assists with drawing a free body diagram.

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