A weather balloon is released and rises vertically such that its distance s(t) above the ground during the first 10 seconds of the flight is given by s(t) = 7 + 2t + t^2, where s(t) is in feet and t is in seconds.

a) Find the velocity of the balloon at t=1, t=4
b) Find the velocity and acceleration (in proper units) at the instant the balloon is 51 feet above the ground.

Question

A weather balloon is released and rises vertically such that its distance s(t) above the ground during the first 10 seconds of the flight is given by s(t) = 7 + 2t + t^2, where s(t) is in feet and t is in seconds. 

a) Find the velocity of the balloon at t=1, t=4
b) Find the velocity and acceleration (in proper units) at the instant the balloon is 51 feet above the ground.

lgbasallote · Answer

are you familiar with derivatives?

anonymous · Answer

Yes. Would the first thing I do is find s'(t)?

anonymous · Answer

yep

anonymous · Answer

s'(t)= 2t+2 What would I do after that?

anonymous · Answer

find s'(1) and s'(4)

anonymous · Answer

pretty easy...
for the second part..

anonymous · Answer

Okay. For the second part I just do 51=7+2t+t^2 right? then equal to zero and find the roots?

anonymous · Answer

solve for t when s(t) = 51
use that t (call it tf, for fun time) to find s'(tf)  and s''(tf)  (hint: s''(t), aka acceleration, is constant, so it doesn't depend on time anyway)

anonymous · Answer

yes:)  exactly.

anonymous · Answer

Alright! Thanks a lot! :)

anonymous · Answer

sure:)  gl!

anonymous · Answer

To find acceleration I just find the second derivative?

anonymous · Answer

yes.