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A bullet fired from a rifle has an initial velocity of $$v=700\text{ ms}^-1$$. Drag force from the air on the bullet causes an acceleration of $$-3v^2$$. How long will this bullet take to reach a target $$1500\text{ m}$$ away horizontally? Clarification: There are no other forces acting on the bullet.

Note by A Brilliant Member
2 years, 1 month ago

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\begin{align}\frac{\mathrm{d}v}{\mathrm{d}t} &= -3 v^2 \\\implies \frac{1}{v}- \frac{1}{700}&=3t \\\implies x &= \frac{1}{3} \ln (1+2100t)\\ \text{Given: } x&=1500\, m \\\implies t &\approx 10^{1951} \ s\end{align}

- 2 years, 1 month ago

Do we neglect gravity?

- 2 years, 1 month ago

Yes.

- 2 years, 1 month ago

I do not understand what v is in the acceleration. Just use the second equation of motion and solve.

- 2 years, 1 month ago

v is the speed of the bullet in that moment

- 2 years, 1 month ago