Predict how the range of the projectile will change when you change the angle from 45∘, keeping the speed constant.
A The range increases with increase in angle and decreases with decrease in angle.
B It increases with either an increase or decrease in angle.
C It decreases with either an increase or a decrease in angle.
D The range increases with decrease in angle and decreases with increase in angle.
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To predict how the range of a projectile will change when you change the angle from 45 degrees while keeping the speed constant, you need to understand the relationship between the angle and the range.
The range of a projectile is determined by its initial velocity and launch angle. In this scenario, the speed of the projectile is constant, so we can focus on the effect of changing the angle.
To figure out how the range changes with the angle, we can consider the components of the initial velocity in the x and y directions.
When the angle is 45 degrees, the initial velocity is divided equally into the x and y components. As a result, the projectile reaches maximum range.
If we decrease the angle below 45 degrees, such as 30 degrees, it means more of the initial velocity is directed in the horizontal x direction. Therefore, the range will decrease because the vertical y component of the velocity is smaller.
Conversely, if we increase the angle above 45 degrees, such as 60 degrees, more of the initial velocity is directed in the vertical y direction. This will also result in a decrease in range since the horizontal x component of the velocity decreases.
From this analysis, we can conclude that the range increases with a decrease in the angle and decreases with an increase in the angle.
Therefore, the correct answer is option D: The range increases with a decrease in the angle and decreases with an increase in the angle.