A) the two bullets will be at the same height above the ground at t = 12.5 s.
B) the two bullets will reach back their stating point at t = 25 s.
C) the two bullets will have the same speed at t = 20 s.
D) the maximum height attained by either bullet will be 980 m.
Correct Answer: A
Solution :
The two bullets will be at the same height at \[t=n\]if \[98-4.9\,{{n}^{2}}=98(n-5)-4.9\,{{(n-5)}^{2}}.\] This gives\[~n=12.5\text{ }s.\]The time to reach the highest point is given by 0 = 98 - 9.8 t, i.e., t = 10 sec. Therefore, the time of flight is \[2\times 10\,s\] or 20 sec. The speed of the first bullet at t = 20 sec. is 98 m/s again while that of the second bullet is \[(98-9.8\times 0.5)\,m/s\]or 49 m/s. The maximum heights attained are 490 m each. Hence, the correction option is [a].
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