Final answer:
The time taken for a ball to land is independent of its horizontal velocity and is determined by its vertical fall under gravity. It will take approximately 10 seconds to fall from a height of 490m. The range of the ball, given a horizontal velocity of 200 m/s, will be 2000 m.
Step-by-step explanation:
The time a ball takes to land when dropped from a certain height is determined by its vertical motion, which is independent of its horizontal velocity. The equation to calculate the fall time (t) from a height (h) in meters when acceleration due to gravity (g) is 9.8 m/s², is obtained by rearranging the equation h = 1/2 g t² to solve for t:
t = √(2h/g)
For a height of 490m, the calculation yields t = √(2*490/9.8) which is approximately 10 seconds, so the correct option is (b) Time = 10 s.
For the range, we use the horizontal velocity (vx) and the time of flight (t) to find the horizontal distance (R) the ball travels:
R = vx × t
With a horizontal velocity of 200 m/s and a time of flight of 10 seconds, the range is:
R = 200 m/s × 10 s = 2000 m, and the correct option is (b) Range = 2000 m.