Question

8 mark for review two identical balls, ball 1 and ball 2, are hit from the same initial position and move along the trajectories shown in the figure. the initial speed of ball 1 is less than that of ball 2. which ball takes less time to return to the ground, and what evidence supports this claim? a ball 1 takes less time. its initial speed is less than that of ball 2. b ball 1 takes less time. the horizontal distance it travels is less than that of ball 2. c ball 2 takes less time. its initial speed is greater than that of ball 1. d ball 2 takes less time. the maximum height it reaches is less than that of ball 1.

Explanation:

Step1: Analyze vertical - motion time formula

The time - of - flight \(t\) of a projectile (in the absence of air resistance) is given by the formula \(t = \frac{2v_{0y}}{g}\), where \(v_{0y}\) is the initial vertical component of velocity and \(g\) is the acceleration due to gravity. The maximum height \(H=\frac{v_{0y}^{2}}{2g}\), so \(v_{0y}=\sqrt{2gH}\). The time of flight is related to the maximum height.

Step2: Compare maximum heights

From the figure, Ball 1 reaches a higher maximum height than Ball 2. Since \(t=\frac{2v_{0y}}{g}\) and \(v_{0y}=\sqrt{2gH}\), a higher maximum height means a larger initial vertical component of velocity and a longer time - of - flight. So Ball 2, which has a lower maximum height, takes less time to return to the ground.

Answer:

D. Ball 2 takes less time. The maximum height it reaches is less than that of Ball 1.