Question

A bullet blasts from the barrel of gun upwards in the vertical direction with an initial speed of 700m/s. Find the maximum altitude reached by this bullet and the time needed to reach it. (g= 10m/s^2)

Answer 1

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The initial velocity (u) will be 700 m/s
The final velocity (v) will be 0, as when the bullet reaches maximum height, it will stop. And start falling down.
Since acceleration due to gravity here is working downwards, we will take g as - 10 m/s²

Let maximum height be S and time taken be t.

v²-u² = -2gS
0²-700² = -2×10×S
S = 490000/20
= 24500 m
Quite some height.
S = ut - ½gt²
24500 = 700t - ½×10×t²
5t²-700t+24500 = 0
t²-140t+4900 = 0
(t-70)² = 0
t = 70 s.

So the bullet will go to a height of 24.5 km or 24500 m and it will take 1 minute 10 seconds, or 70 seconds to reach there.

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