1) A hot air balloon begins to rise from rest. The lift on the balloon due to the buoyant force is 5000 N. a) If the total mass of the balloon and everything that it is lifting is 500 kg, then what is the acceleration of the balloon? After rising 10 m, a passenger in the balloon realizes that they forgot their cell phone on the ground and jumps out of the balloon because of separation anxiety. b) What is the acceleration of the balloon after the 70 kg passenger jumps out? c) Supposing that the passenger jumps horizontally, what is the initial velocity of the passenger in the vertical direction at the time of the jump? (It should be the same as the velocity of the balloon at this time.)
1) A hot air balloon begins to rise from rest. The lift on the balloon due to the buoyant force is 5000 N.
a) If the total mass of the balloon and everything that it is lifting is 500 kg, then what is the acceleration of the balloon?
After rising 10 m, a passenger in the balloon realizes that they forgot their cell phone on the ground and jumps out of the balloon because of separation anxiety.
b) What is the acceleration of the balloon after the 70 kg passenger jumps out?
c) Supposing that the passenger jumps horizontally, what is the initial velocity of the passenger in the vertical direction at the time of the jump? (It should be the same as the velocity of the balloon at this time.)
d) What is the vertical component of the passenger’s velocity when they hit the ground after falling 10 m?
e) How much time passes between when the passenger jumps and when they hit the ground?
f) What is the height of the balloon when the passenger reaches the ground?
g) In order to minimize the time until the passenger is reunited with their cell phone, what should the horizontal component of the passenger’s velocity be so that they land directly on their phone which is initially 3 m away in the horizontal direction?
h) If the passenger jumps with this horizontal velocity, then what is the horizontal component of the balloon’s velocity after the jump and how far has the balloon traveled in the horizontal direction when the passenger hits the ground?
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