A girl throws a water-filled balloon at an angle of 50.0∘^\circ above the horizontal with a speed of 12.0m/s{\rm m}/{\rm s} . The horizontal component of the balloon's velocity is directed toward a car that is approaching the girl at a constant speed of 8.00m/s{\rm m}/{\rm s} .If the balloon is to hit the car at the same height at which it leaves her hand, what is the maximum distance the car can be from the girl when the balloon is thrown? You can ignore air resistance.

Answer 1

Vo = 12m/s[50o]
Xo = 12*Cos50 = 7.71 m/s.
Yo = 12*sin50 = 9.19 m/s.

Tr = -Yo/g = -9.19/-9.8 = 0.938 s.

Tf = Tr = 0.938 s. = Fall time.

Tr+Tf = 0.938 + 0.938 = 1.876 s. = Time
to return to launching height.

Range=Xo * (Tr+Tf) = 7.71 * 1.876=14.46m

D max = 14.46 + 8m/s * 1.876s
D max = 14.46 + 15 = 29.5 m.

Answer 2

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