Final answer:
Using the formula for the range of projectile motion, the correct angle to double the range of the soccer ball without exceeding a 45-degree limit and without changing the initial speed is 30 degrees.
Step-by-step explanation:
The problem stated is related to projectile motion in physics and we can use the projectile motion equations to solve it. When we kick a soccer ball at an angle above the horizontal, the range it travels depends on the initial speed and the angle of projection. It is known from physics that the range of a projectile launched with the same speed is maximal at a 45-degree angle. As the student cannot kick the ball at an angle higher than 45 degrees, and the initial range is achieved with a 10-degree angle, we need to find a second angle smaller than 45 degrees that still allows the range to be doubled.
To solve this problem, we use the formula for the range of projectile motion, which is R = (v^2 × sin(2θ)) / g where R is range, v is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity. Since we want to double the range without changing the initial velocity, we look for an angle θ such that sin(2θ) is double that of the initial sin(20 degrees). The correct answer will be 30 degrees, which, when plugged into the formula, gives us a range approximately double that of the initial 10-degree launch angle within the constrain of not exceeding the 45-degree limit.