Solve this and post working

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.

#Mechanics

Easy Math Editor

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Comments

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

A Former Brilliant Member - 5 years ago

v is the speed of the bullet in that moment

Matteo Monzali - 5 years ago

Do we neglect gravity?

A Former Brilliant Member - 5 years ago

Yes.

A Former Brilliant Member - 5 years ago

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

A Former Brilliant Member - 5 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$