Final answer:
The girl will find the ball at the same horizontal position as where she threw it.
Step-by-step explanation:
In this scenario, the girl throws the ball horizontally, relative to herself, with an initial speed of 20 m/s. Since there is no vertical component to the ball's initial velocity, it will undergo a purely horizontal motion. This means that while the hot air balloon is descending, the ball will maintain its horizontal position relative to the girl's throw.
Therefore, when the girl lands, she will find the ball at the same horizontal position as where she threw it. The vertical motion of the hot air balloon does not affect the horizontal motion of the ball.
At a particular instant, a hot air balloon is 100 m in the air and descending at a constant speed of 2.0 m/s. At this exact instant, a girl throws a ball horizontally, relative to herself, with an initial speed of 20 m/s. Upon landing, the girl will find the ball in front of her.
The reason for this is because in the absence of air resistance, the horizontal motion of the ball and the girl (in the balloon) would be unaffected and both would travel at the same horizontal speed. Since the ball and the girl are moving horizontally at the same speed, they stay aligned with each other.
The vertical motion of the ball is independent of its horizontal motion, so while the ball is affected by gravity and hence descends, it does so at the same rate as the balloon since both start descending from rest.