Question

Payload is released at an elevation of 700 m from a hot air balloon that is rising at a rate of 12 m/s

Answer 1

Answer:

Follows are the solution to the given points:

Step-by-step explanation:

Please find the complete question in the attached file.

Given values:

$g= 9.8 \ \frac{m}{s^2}\\\\u= 12 \ \frac{m}{s}\\\\h=700 \ m$

For point a:

$\to V= u-gt$

$\to V = 12 - 9.8t$

For point b:

$\to S(t)= ut- \frac{1}{2}gt^2+h$

$\to S(t) = 11 t - \frac{1}{2}9.8 t^2 + 700$

           $= 11 t - 4.9t^2 + 700$

For point c:

$\ Let, \ \ v(t) = 0 \\\\\to 0= 12- 9.8 t\\\\\to 9.8t= 12\\\\\to t= \frac{12}{9.8}\\\\\to t = 1.22\ sec$

Calculating the highest point:

$\to s (1.22 ) = 12(1.22) - 4.9(1.22)^2 + 700$

$= 12(1.22) - 4.9(1.22)^2 + 700 \\\\ = 14.64 - 4.9(1.4884) + 700 \\\\ = 14.64 - 7.29316+ 700 \\\\ = 7.34684+ 700 \\\\ = 707.34684$

For point d:

$\to s(t) = 0 \to 707.34684 - 4.9t^2=0 \\\\\to 707.34684 = 4.9t^2 \\\\\to t^2=\frac{707.34684}{4.9} \\\\\to t^2= 144.356498\\\\\to t = 12.01 \ sec\\\\\bold{ \to \text{total time} = 12.01 + 1.22 = 13.23 \ \ sec}$