2013澳大利亚高考数学试题答案(14)

Question 15 (continued)

(d) A ball of mass m is projected vertically into the air from the ground with initial

velocity u. After reaching the maximum height H it falls back to the ground. While in the air, the ball experiences a resistive force kv2, where v is the velocity of the ball and k is a constant.

The equation of motion when the ball falls can be written as

mv = mg kv2

.

(Do NOT prove this.)

(i) Show that the terminal velocity vT

(ii) Show that when the ball goes up, the maximum height H is

2H = v 2

T

u

2 g ln 1+v 2 T

.

(iii) When the ball falls from height H it hits the ground with velocity w.

Show that

1

1

w2

=

u2 + 1 v 2. T

End of Question 15

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