Final answer:
The ball fired horizontally from a cannon will have dropped 510 m by the time the vertical component of its velocity equals the horizontal component, given that the initial horizontal velocity is 100 m/s and there is no air friction.
Step-by-step explanation:
The student's question is about projectile motion, specifically the situation where a cannon fires a ball horizontally off a cliff and we are asked to determine when the magnitude of the vertical component of its velocity is equal to its horizontal velocity component. Since we are neglecting air friction, the horizontal component of velocity will remain constant at 100 m/s. For the vertical motion, we use the equation of motion under gravity, v = gt, where v is the vertical velocity, g is the acceleration due to gravity (9.8 m/s2), and t is the time elapsed.
To find when the vertical component equals 100 m/s, we set v to 100 m/s and solve for t: t = 100 m/s / 9.8 m/s2 ≈ 10.2 s. We then use this time to calculate the distance it falls using the formula s = (1/2)gt2,
Plugging in the values, s = (1/2) * (9.8 m/s2) * (10.2 s)2 = 510 m. Therefore, the ball will have dropped 510 m when its vertical velocity component equals the horizontal component. So the answer is (b) 510 m.