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Vectors and matrices — Question 14

QCAA 2021, Paper 1 · 6 marks

Q14 · 2021 · Technology-freeSimple familiar6 marks

QUESTION 14 (6 marks)

An object is projected vertically upwards from ground level. After the object has been in motion for tt seconds, its position vector through the air, in metres, is modelled by r(t)=5t(8−t)j^.\mathbf r(t)=5t(8-t)\hat{\mathbf j}.
a)
Determine the velocity of the object through the air, v(t)\mathbf v(t), in metres per second.
[2 marks]
b)
Determine the number of seconds until the object reaches its maximum height.
[2 marks]
c)
Determine the maximum height that the object reaches, in metres.
[2 marks]
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