Question

a skydiver jumps out of a plane waering a suit and decleration due to air i s 0.45 m/s^2 for each 1 m/s, skydyvers initial value problems that models the skydiver velocity is v(t). temrinal speed assuming that accelration due to gravity is 9.8m/s

Answer 1

Answer:

$v = 21.77\ m/s$

Explanation:

Given,

Air resistance, = 0.45 m/s² for each 1 m/s

Air resistance for velocity v = 0.45 v.

Terminal velocity = ?

acceleration due to gravity= g = 9.8 m/s²

 now,

a = 0.45 v

we know,

$a =\dfrac{dv}{dt}$

$\dfrac{dv}{dt}=0.45 v$

$\dfrac{dv}{v} = 0.45 dt$

integrating both side

$\int \dfrac{dv}{v} = 0.45\int dt$

$ln(v) = 0.45 t$

$t = e^{0.45 t}$

When a body is moving at terminal velocity, Force due to gravity is equal to  force due to air resistance.

 m a = m g

    0.45 v = 9.8

     $v = \dfrac{9.8}{0.45}$

    $v = 21.77\ m/s$

Hence, the terminal velocity of the skydiver is equal to 21.77 m/s.