This question involves the concepts of projectile motion and launch speed.
(a) The initial launch speed of the projectile is "100 m/s".
(b) The launch angle of the projectile is "53.13°".
<h3>(a) LAUNCH SPEED</h3>
A projectile motion is a motion that takes place on both x and y axes, simultaneously. In this motion the initial launch speed is given by the following formula:

where,
= initial launch speed = ?
= horizontal component of initial launch speed = 60 m/s
= vertical component of initial launch speed = 80 m/s
Therefore,

<h3>(b) LAUNCH ANGLE</h3>
Launch angle is given by th following formula:

Learn more about the projectile motion here:
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Joules is a unit for work which may decomposed into N.m. Work is a quantity which is a product of force (in this case, the woman's weight) and the distance she has traveled.
W = F x d ; d = W / F
Substituting the given,
d = (3.5 x 10^4 J) / (55 kg x 9.8 m/s²) = 64.94 m
Thus, the woman can climb up to 64.94 meters.
B. Half a centimeter per year
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Answer: b
Explanation: the two pieces will repel as both have obtained a static charge.
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