The position of a kite is given by r(t)=t/8i-3/64t(t-160)j where t=0 is measured in seconds and distance is measured in meters. At what time does the kite start to lose altitude?

Question

The position of a kite is given by r(t)=t/8i-3/64t(t-160)j where t>=0 is measured in seconds and distance is measured in meters. At what time does the kite start to lose altitude?

anonymous · Answer

missing a j?

anonymous · Answer

theres a j at the end there lol

anonymous · Answer

The thing is that the i value doesn't influence j (unless there are mountains we don't know about).  So we just have y = -3/64t(t-160)
which we have to differentiate
dy/dt = ?

anonymous · Answer

that whole part goes together

anonymous · Answer

We need to know y(t), we don't care about x.

anonymous · Answer

yea i follow you thanks!

anonymous · Answer

Can you differentiate?

anonymous · Answer

lol yes so do i just differentiate the j part with respect to t?

anonymous · Answer

Yep.

anonymous · Answer

thanks then after that i solve for t?

anonymous · Answer

-3/64(2t - 160) = ?

anonymous · Answer

i got -3/32(t-80) as the derivative then just solve for t right?

anonymous · Answer

You need to multiply the single t inside the parentheses
At least, that's the easiest way.

anonymous · Answer

so i got t=5/64 or .078 is that right?

anonymous · Answer

I'll let you do the arithmetic.  The important part is to ignore x, then differentiate correctly and set equal to 0.

anonymous · Answer

alright i think im good then thank you for your help!