Question

You are in a hot-air balloon that ascends at a constant velocity of 2.75 m/s for 10

minutes. Your combined mass, you, the balloon and all of the balloon’s hardware, is

1350 kg. How much work is done against gravity during this ascent? What is the change

in the gravitational potential energy of the hot-air balloon system? If you drop an object

out of the balloon at rest with respect to the balloon, at what speed will it just strike the

ground!

PLEASE ANSWER ALL PARTS AND EXPLAIN THANK YOU. I AM GETTING MULTIPLE ANSWERS SO PLEASE DO CORRECTLY.

Answer 1

v = speed = 2.75 m/s

t = time of travel = 10 min = 10 x 60 sec = 600 sec

distance traveled is given as

d = v t = 2.75 x 600 = 1650 sec

m = mass = 1350 kg

work done is given as

W = mg d

W = (1350)(9.8)(1650)

W = 21829500 J

Change in gravitational potential energy = W = 21829500 J

vo = initial velocity = 2.75 m/s

v = final velocity = ?

d = displacement = 1650 m

a = acceleration = 9.8 m/s2

Using the equation

v2 = vo2 + 2 a d

v2 = 2.752 + 2 (9.8) (1650)

v = 179.85 m/s