- #1

Shreya

- 188

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- Homework Statement
- A Balloon moves up at 25m/s, 5 seconds later a bullet is fired in the same direction. Find the minimum velocity of the bullet such that it pops the balloon.

- Relevant Equations
- $$v=u+at$$

$$s=ut+\frac {1}{2} at²$$

$$s=\frac{1}{2} (u+v)t$$

$$v²=u²+2as$$

Where:

$$s=25t + 125$$

$$v = 25m/s$$

$$a=10$$

I can solve this question using relative Velocity or using 2 kinematics equations. But a peer of mine, tried to do it in a different way. He substituted the above said values in the 4 equations and solved for u in terms of t and differentiated them and equated to to 0 to find a maxima. He found that for the 1, 3 and 4th equations, there was no value of t for which u was minimum but the 2nd equation gave the right answer.

Here's a graph of the 4 equations.

The question is - why did the second function have a minima while others didn't.

Please be kind to help!

Here's a graph of the 4 equations.

The question is - why did the second function have a minima while others didn't.

Please be kind to help!

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