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

Follows are the solution to the given points:

Explanation:

Please find the complete question in the attached file.

Given values:

`g= 9.8 \ (m)/(s^2)\\\\u= 12 \ (m)/(s)\\\\h=700 \ m`

For point a:

`\to V= u-gt`

`\to V = 12 - 9.8t`

For point b:

`\to S(t)= ut- (1)/(2)gt^2+h`

`\to S(t) = 11 t - (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= (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=(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}`