fisica1-youn-e-freedman-exercicios-resolvidos

3.85: The three relative velocities are:
v r Juan relative to the ground. This velocity is due north and has magnitude
v
J/G,
J/G
B/G,
= 8.00 m/s.
v r the ball relative to the ground. This vector is 37 .0°
east of north and has magnitude
v B/G
= 12.0 m/s.
v r
B/J,
the ball relative to Juan. We are asked to find the magnitude and direction of this
vector.
r r r r r r
The relative velocity addition equation is v
B/G
= v
B/J
+ v
J/G,
so v
B/J
= vB/G
− v
J/G.
Take + y to be north and + x to be east.
= + v sin 37.0°
7.222 m/s
vB/J x B/G
=
v cos B/J y
= + vB/G 37.0° − v J / G
=
1.584 m/s
These two components give v = 7.39 m/s at 12 .4°
north of east.
B/J
2
3.86: a) v y
= 2gh
= 2(9.80 m/s )(4.90 m) 9.80 m/s. b) v y
/ g 1.00 s.
c) The
0
=
0
=
2
2
speed relative to the man is (10.8 m/s) − (9.80 m/s) = 4.54 m/s,
and the speed relative
to the hoop is 13.6 m/s (rounding to three figures), and so the man must be 13.6 m in
front of the hoop at release. d) Relative to the flat car, the ball is projected at an angle
−1
m/s
tan
9.80
−1
9.80 m/s
θ =
= 65°
Relative to the ground the angle is θ tan ( ) = 35.7°
( ) .
4.54 m/s
2
2
3.87: a) (150 m/s) sin 2°
/9.80 m/s = 80 m.
−2
π (10×
10 m)
−3
b) 1000×
= 1.6 × 10 .
2
π (80 m)
2
=
4.54 m/s+
9.10 m/s
c) The slower rise will tend to reduce the time in the air and hence reduce the radius.
The slower horizontal velocity will also reduce the radius. The lower speed would tend
to increase the time of descent, hence increasing the radius. As the bullets fall, the friction
effect is smaller than when they were rising, and the overall effect is to decrease the
radius.
2
3.88: Write an expression for the square of the distance ( D ) from the origin to the
2
particle, expressed as a function of time. Then take the derivative of D with respect to t,
and solve for the value of t when this derivative is zero. If the discriminant is zero or
−
negative, the distance D will never decrease. Following this process, sin 1 8/9 = 70.5°
.