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Question

At time t=0, a bullet is fired vertically upwards with a speed of 98 ms1. At time t=5 s (i.e., 5 seconds later) a second bullet is fired vertically upwards with the same speed. If the air resistance is neglected, which of the following statements is/are true?

A
The two bullets will be at the same height above the ground at t=12.5 s.
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B
The two bullets will reach back their starting points at the same time.
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C
The two bullets will have the same speed at t=20sec.
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D
The two bullets will attain the same maximum height.
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Solution

The correct options are
A The two bullets will be at the same height above the ground at t=12.5 s.
D The two bullets will attain the same maximum height.
For first bullet,
Time of ascent =ug=989.8=10 s (Using first equation of motion)
After 12.5 s, position of 1st bullet from the ground
=98×1251012×9.8×(12.5)2=459.375 m
As the second bullet is fired 5 s later than 1st bullet, t=(12.55)=7.5 s
Using second equation of motion, we get
=98×751012×9810×(75)2100=459.375 m

Hence, it is clear that position of both the bullets will be at same height at t=12.5 s.

Maximum height in case of motion under gravity neglecting air resistance depends only on initial velocity. So the two bullets will attain the same maximum height.

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