# Question #40306

Nov 16, 2016

The mass of the man $= 76 k g$
The downward gravitational force on him
$= 76 \times g N = 76 \times 9.8 N = 744.8 N$

The mass of the Parachute $= 5.5 k g$
The downward gravitational force on it
$= 5.5 \times g N = 5.5 \times 9.8 N = 53.9 N$

So total downward gravitational pull
${F}_{g} \downarrow = \left(744.8 + 53.9\right) N = 798.7 N$

The net downward acceleration on the system is $2.6 m {s}^{-} 2$

So the net downward force

${F}_{n} \downarrow = \left(76 + 5.5\right) \times 2.6 = 211.9 N$

Now

${F}_{n} \downarrow = {F}_{g} \downarrow - {F}_{\text{air}} \uparrow$

$\implies {F}_{\text{air}} \uparrow = {F}_{g} \downarrow - {F}_{n} \downarrow$

$\implies {F}_{\text{air}} \uparrow = 798.7 - 211.9 = 586.8 N$

(a) The upward force exerted on the open parachute by the air$= {F}_{\text{air}} \uparrow = 586.8 N$

(b) The downward force exerted by the person on the parachute $= 744.8 N$