Question

An animal-rescue plane flying due east at 55 m/s drops a bale of hay from an altitude of 69 m . The acceleration due to gravity is 9.81 m/s 2 . If the bale of hay weighs 192 N , what is the momentum of the bale the moment it strikes the ground?

Answer 1

Answer:

The momentum of the bale the moment it strikes the ground is 1076.68 kg-m/s.

Explanation:

It is given that,

Velocity of an animal-rescue plane, $v_x=55\ m/s$

It drops a bale of hay from an altitude of 69 m, h = 69 m

The vertical velocity of plane is given by :

$v_y=\sqrt{2gh}$

$v_y=\sqrt{2\times 9.81\times 69} =36.79\ m/s$

Weight of the bale of hay, W = 192 N

If m is the mass, then weight is given by :

$m=\dfrac{W}{g}$

$m=\dfrac{192}{9.81}=19.57\ kg$

The resultant momentum of the bale the moment it strikes the ground is given by :

$p=m(v_x-v_y)$

$p=19.57\times 55i-19.57\times 36.79j$

$p=(1076.35i-719.98j)\ kg-m/s$

Magnitude of momentum,

$p=\sqrt{1076.35^{2}+719.98}$

p = 1076.68 kg-m/s

So, the momentum of the bale the moment it strikes the ground is 1076.68 kg-m/s. Hence, this is the required solution.