Final answer:
When a projectile's initial velocity is doubled while keeping the projection angle constant, the horizontal range is quadrupled. This is due to the relationship R' = 4 * (v^2/g) * sin(2θ), as per the formula for the range of projectile motion.
Step-by-step explanation:
The question asks about the effect on horizontal range if a projectile's initial velocity is doubled while keeping the angle of projection the same. The formula for horizontal range R in projectile motion is given by R = (v^2/g) * sin(2θ), where v is the initial velocity, g is the acceleration due to gravity, and θ is the angle of projection. Doubling the initial velocity (2v) in this equation gives R' = ((2v)^2/g) * sin(2θ), which simplifies to 4 * (v^2/g) * sin(2θ). Therefore, R' is four times R, meaning the range would be quadrupled.
The correct answer to the student's question is: d) It will be quadrupled.
Additionally, to address the GRASP CHECK related to the change in time of flight when only the horizontal component of velocity is doubled, the answer would be: a) The time to reach the ground would remain the same since the vertical component is unchanged.