A flare is launched from a hot-air ballon and moves in a vertical . At time t seconds the height of the flare is X metres , where x=1664-40t-(2560/t) for t=5. The flare is launched when t=5.
Find the terminal speed of the flare

Question

A flare is launched from a hot-air ballon and moves in a vertical . At time t seconds the height of the flare is X metres , where x=1664-40t-(2560/t) for t>=5. The flare is launched when t=5.
Find the terminal speed of the flare

anonymous · Answer

@experimentX  PLZ HELP

experimentx · Answer

what is x?

anonymous · Answer

height of the flare from the ground

experimentx · Answer

http://www.wolframalpha.com/input/?i=plot+1664-40t-%282560%2Ft%29+from+0+to+40 the slope is almost constant. we need to find the slope of the line.

experimentx · Answer

what would be the behavior ... as x-> infinity ?

anonymous · Answer

x cannot be infinity because after it reaches a maximum height it will start to fall

experimentx · Answer

sorry, t-> infinity
the velocity will be constant as t->inf ... the slope will be -40 ... so this is your terminal velocity.

anonymous · Answer

@experimentX  u got the correct answer........Can u explain how? plz.... why t approaches infinity

anonymous · Answer

@experimentX  r u free

anonymous · Answer

@mukushla  can u help...... PLZ

anonymous · Answer

he used derivative, v=x'. the velocity is actually the slope of the graph

anonymous · Answer

an object reaches to its terminal velocity when It's acceleration drops to 0 and the velocity stays constant.

u have $$ x=1664-40t-\frac{2560}{t}$$ so $$u=\frac{dx}{dt}=-40+\frac{2560}{t^2}$$now note that $u=$constant when  $t \rightarrow \infty$

anonymous · Answer

oh....... terminal speed means the speed when the speed is constant

anonymous · Answer

yeah...

anonymous · Answer

I thought terminal speed was the speed of the flare just before it touches the ground.

experimentx · Answer

yep ... !!

anonymous · Answer

But why do we take t approaches infinity

anonymous · Answer

@experimentX

experimentx · Answer

because you would get a constant speed as t->inf ...  this factor (2560/t) -> 0 as t-> inf

anonymous · Answer

but the flare will not be in the air for infinite time

experimentx · Answer

yeah ... everything is based on approximation there isn't such thing as infinity ... just  t >> 2560 means 2560/t == 0

anonymous · Answer

oh..... so actually the flare will not reach its terminal speed.. practically

anonymous · Answer

right? @experimentX

experimentx · Answer

there is not such thing as exact in physics. Everything is an approximation.

anonymous · Answer

thanx to all who helped..........