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Date November 2020 Marks available 3 Reference code 20N.1.SL.TZ0.T_12
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number T_12 Adapted from N/A

Question

Jean-Pierre jumps out of an airplane that is flying at constant altitude. Before opening his parachute, he goes through a period of freefall.

Jean-Pierre’s vertical speed during the time of freefall, S, in m s-1, is modelled by the following function.

St=K-601.2-t , t0

where t, is the number of seconds after he jumps out of the airplane, and K is a constant. A sketch of Jean-Pierre’s vertical speed against time is shown below.

Jean-Pierre’s initial vertical speed is 0m s-1.

Find the value of K.

[2]
a.

In the context of the model, state what the horizontal asymptote represents.

[1]
b.

Find Jean-Pierre’s vertical speed after 10 seconds. Give your answer in kmh1 .

[3]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

0=K-601.20      (M1)


Note:
Award (M1) for correctly substituted function equated to zero.


K= 60      (A1)    (C2)


[2 marks]

a.

the (vertical) speed that Jean-Pierre is approaching (as t increases)     (A1)    (C1)
OR
the limit of the (vertical) speed of Jean-Pierre     (A1)    (C1)


Note: Accept “maximum speed” or “terminal speed”.


[1 mark]

b.

S= 60-601.2-10     (M1)


Note: Award (M1) for correctly substituted function.


S= 50.3096m s-1     (A1)(ft)


Note:
Follow through from part (a).


181 km h-1  181.114km h-1     (A1)(ft)       (C3)


Note: Award the final (A1)(ft) for correct conversion of their speed to kmh1.


[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 2—Functions » SL 2.5—Modelling functions
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