hot-air balloon is ascending at the rate of 14 m/s and is 84 m above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?

a) t = 4.14 s

b) Speed with which it hits the ground = 40.58 m/s

Explanation:

Using the equations of motion,

g = 9.8 m/s², y = H = 84 m,

Initial velocity, u = 0 m/s,

final velocity, v = ?

Total Time of fall, t = ?

a) y = ut + gt²/2

84 = 0 + 9.8t²/2

4.9t² = 84

t² = 84/4.9

t = 4.14 s

b) v = u + gt

v = 0 + (9.8 * 4.14)

v = 40.58 m/s

A. t = 4.14 s.

B. 40.62 m/s.

Explanation:

Using the equations of motion,

Given:

g = 9.8 m/s²

S = 84 m,

S = vo*t + (a*t²) / 2

vo = initial velocity

= 0 m/s

vi = final velocity

t = Time of motion

84 = 0 + (9.8*t²) / 2

t² = 84/4.9

= sqrt (17.143)

t = 4.14 s.

B.

vi = vo + a*t

= 0 + (9.81 * 4.14)

= 40.62 m/s.