Question

At a particular instant, a hot air balloon is 150 m in the air and descending at a constant speed of 5.0 m/s. At this exact instant, a girl throws a ball horizontally, relative to herself, with an initial speed of 25 m/s. When she lands, where will she find the ball?

Answer 1

The ball will land approximately 101.4 meters away from the girl.

Step-by-step explanation:

To find where the girl will find the ball, we need to determine the time it takes for the ball to reach the ground. Since the ball is thrown horizontally, its initial vertical velocity is 0 m/s. We can use the formula h = 1/2 * g * t^2, where h is the initial height, g is the acceleration due to gravity, and t is the time. Plugging in the values, we get 150 = 1/2 * 9.8 * t^2. Solving for t, we find that it takes approximately 5.07 seconds for the ball to reach the ground.

Now we can find the horizontal distance the ball travels using the formula d = v * t, where d is the distance, v is the horizontal speed of the ball, and t is the time. In this case, the horizontal speed is 20 m/s and the time is 5.07 seconds. Plugging in the values, we get d = 20 * 5.07 = 101.4 meters. Therefore, the girl will find the ball approximately 101.4 meters away from her.