Question

Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of 0.5 ft3/s. Initially, the balloon has 2 ft3 of hydrogen.(a) Find a linear function V that models the volume of hydrogen in the balloon at any time t.V(t) = (b) If the balloon has a capacity of 15 ft3, how long does it take to completely fill the balloon?

Answer 1

Answer:

a) A linear function V that models the volume of hydrogen in the balloon at any time t.

$V(t)=0.5\times t+2$

b) It will take 26 seconds to fill the balloon with hydrogen gas upto 15 cubic feet volume.

Step-by-step explanation:

a) Volume of hydrogen gas present initially ion balloon = $2 ft^3$

Rate at which hydrogen gas is filled = $0.5 ft^3/s$

Volume of the hydrogen gas after time t = V

$V=0.5ft^3/s\times t+2ft^3$

A linear function V that models the volume of hydrogen in the balloon at any time t.

$V(t)=0.5\times t+2$

b) Maximum volume capacity of the balloon = V = $15 ft^3$

Time taken to fill the balloon upto its maximum capacity = t

$V(t)=0.5\times t+2$

$V(t)=15=0.5\times t+2$

$15-2=0.5\times t$

$t=\frac{13}{0.5}=26$

$V(26)= 15 ft^3$

It will take 26 seconds to fill the balloon with hydrogen gas upto 15 cubic feet volume.