Question

A small mailbag is released from a helicopter that is descending steadily at 2.77 m/s.

(a) After 4.00 s, what is the speed of the mailbag?

(b) How far is it below the helicopter?

(c) What are your answers to parts (a) and (b) if the helicopter is rising steadily at 2.77 m/s?

Answer 1

(a) the speed of the mailbag after 4 sec which will be given as :

using equation of motion 1,     v = v₀ + gt                                                                      { eq.1 }

where, v₀ = initial velocity = 2.77 m/s

g = acceleration due to gravity = 9.8 m/s²

inserting these values in above eq.

v = (2.77 m/s) + (9.8 m/s²) (4 s)

v = 41.9 m/s

(b) At a distance, it below the helicopter which is given as :

using equation of motion 2, x₁ = v₀ t + (1/2) g t²                                                                       { eq.2 }

where, x₁ = distance travelled

inserting the values in eq.2,

x₁ = (2.77 m/s) (4 s) + (0.5) (9.8 m/s²) (4 s)²

x₁ = (11.08 m) + (78.4 m)

x₁ = 89.48 m

since, the helicopter also moves downward at the same time which given as :

x₂ = v₀ t                                                                                        { eq.3 }

inserting the values in eq.3,

x₂ = (2.77 m/s) (4 s)

x₂ = 11.08 m

distance between the mailbag and helicopter is given as,   d = x₁ - x₂

then     d = (89.48 m) - (11.08 m)

d = 78.4 m

(c) if the helicopter is rising steadily at 2.77 m/s, then answers to part (a) & (b) which will be given as ::

we have an initial velocity, v₀ = - 2.77 m/s

using a same formula, v = v₀ + gt (-2.77 m/s) + (9.8 m/s²) (4 s)

v = - 36.4 m/s         

And for part-b :    x₁ = v₀ t + (1/2) g t²                

x₁ = (-2.77 m/s) (4 s) + (0.5) (9.8 m/s²) (4 s)²

x₁ = (-11.08 m) + (78.4 m)

x₁ = 67.32 m

since, the helicopter also moves downward at the same time which given as :

x₂ = v₀ t (-2.77 m/s) (4 s)                                                                         

x₂ = -11.08 m

distance between the mailbag and helicopter is given as,   d = x₁ - x₂

then     d = (67.32 m) + (11.08 m)

d = 78.4 m