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Solution 8.5b

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From part a) we have

v=(80+t )i+4t j.

and

r=(80t+21t 2 )i+2t 2 j


We see the height is

Thus the time when the aeroplane is at a height 50 m.

We see the height is 2t 2 for any time t.

Thus the time when the aeroplane is at a height 50 m is given by

2t 2=50

or

t=5 s

At this time the velocity is

v=(80+5)i+45 j=85i+20j

The speed is the magnitude of this velocity


852+202=87.3 ms−1 

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