Final answer:
The angle of impact cannot be accurately determined with the provided information, as we would need the time it takes for the bottle to fall to calculate the horizontal distance and subsequently the angle using trigonometry.
Step-by-step explanation:
The child is in a car travelling at 14 m/s and drops a bottle. To determine the angle at which the bottle hits the ground, we need to consider the vertical and horizontal components of the bottle's motion separately. Because air resistance is ignored, the horizontal velocity remains constant at 14 m/s. The vertical motion is affected by gravity and can be calculated using kinematic equations. However, with the information provided, it is not possible to determine the exact angle without knowing the time it takes for the bottle to hit the ground. Typically, to find the time, we would use the equation s = ut + (1/2)at^2, where s is the displacement (1.6 m in this case), u is the initial velocity (0 m/s, since it's being dropped), a is the acceleration due to gravity (9.81 m/s^2), and t is the time.
Using this equation, we solve for t to find the time it takes for the bottle to fall. Once we have the time, we can then calculate the horizontal distance traveled and use trigonometry to find the angle at which the bottle hits the ground. It is also important to note that in a realistic scenario, air resistance cannot be ignored and would affect both the time of flight and the angle of impact. For academic exercises like this, ignoring air resistance simplifies the calculation and focuses on understanding basic principles of projectile motion.