A hot-air balloon is ascending at the rate of 10 m/s and is 74 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?

The answer to your question is:

a) t1 = 2.99 s ≈ 3 s

b) vf = 39.43 m/s

Explanation:

Data

vo = 10 m/s

h = 74 m

g = 9.81 m/s

t = ? time to reach the ground

vf = ? final speed

a) h = vot + (1/2) gt²

74 = 10t + (1/2) 9.81t²

4.9t² + 10t - 74 = 0 solve by using quadratic formula

t = (-b ± √ (b² - 4ac) / 2a

t = (-10 ± √ (10² - 4 (4.9 (-74) / 2 (4.9)

t = (-10 ± √ 1550.4) / 9.81

t1 = (-10 + √ 1550.4) / 9.81 t2 = (-10 - √ 1550.4) / 9.81

t1 = (-10 ± 39.38) / 9.81 t2 = (-10 - 39.38) / 9.81

t1 = 2.99 s ≈ 3 s t2 = is negative then is wrong there are

no negative times.

b) Formula vf = vo + gt

vf = 10 + (9.81) (3)

vf = 10 + 29.43

vf = 39.43 m/s