Question

You wad up a piece of paper and throw it into the wastebasket. How far will

Answer 1

Answer:

Since the paper is wadded up tight, and if there's any

air resistance left we assume there isn't any, it might

just as well be a stone that's tossed.  This is just a

stripped down projectile situation.

You said "an angle of 36 degrees", but you didn't say relative

to what.  I'll assume that it's 36 degrees above horizontal, and

now I'll proceed to answer the question with the information that

I just gave myself.

-- The vertical component of the velocity is  1.4 sin(36)

                                                                        = 0.823 m/s up.

-- The projectile rises for (0.823/9.8) second, runs out of gas,

and then falls for another (0.823/9.8) second to its original height.

So it's in the air for

                                  2 (0.823/9.8) = 0.168 second

                                                            (not very long at all)

-- The horizontal component of the velocity is  1.4 cos(36)

                                                                           = 1.133 m/s  

                                                             and it doesn't change.

-- During the 0.168 second that it's in the air,

the wad travels horizontally

                                              (0.168 s) x (1.133 m/s)

                                          =            0.19 meter

                                              (19 cm, ~ 7.5 inches)

If you find my mistake on this one, please please tell me.  

As of now, it looks like with that velocity at that angle, your

paper wad only makes it 7.5 inches from your hand into the can.

Explanation:

Answer 2

I used this kinematics equation:
H = Vt + 0.5At^2
H is height, t is time, V is initial vertical velocity, and A is acceleration.
Given values:
V = 3.1sin(32) = 1.643m/s
A = -9.81m/s^2
H = 1.643t - 4.905t^2
Solve for t when H = 0:
1.643t - 4.905t^2 = 0
t = 0.3349, 0
Reject t = 0
t = 0.3349s

Use this to calculate horizontal displacement:
X = Vt
X is horizontal displacement, V is horizontal velocity, and t is time.
Given values:
V = 3.1xcos(32) = 2.629m/s
t = 0.3349s
X = 2.629x0.3349
X = 0.88m

Choice C.