# How do I solve a rate of reaction problem? [closed]

A bullet is fired in the air vertically from ground level with an initial velocity 282 m/s. Find the bullet's maximum velocity and maximum height.

For this problem I don't even know where to begin. I do know that I need to identify relevant numbers and create equations based off of that , however, I don't know how to proceed after.

Thank you for your time! You rock guys xoxo

## closed as off-topic by SchrodingersCat, Thomas, Najib Idrissi, Claude Leibovici, Mark ViolaDec 9 '15 at 16:03

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• Where are you standing/sitting/anything will firing the bullet? (It will have different outcomes on different positions on Earth, in universe, for example in a black hole...) – Aditya Agarwal Dec 9 '15 at 13:58
• I'm joking , please – Mone Skratt Henry Dec 9 '15 at 14:05
• Actually I'm on Earth! Thnaks – Mone Skratt Henry Dec 9 '15 at 14:07
• This is a Physics problem. – Ramiro Dec 9 '15 at 15:14
• Well it was covered in my calc class :D – Mone Skratt Henry Dec 9 '15 at 19:50

## 2 Answers

To begin, we know that the bullets maximum velocity is 282 m/s; and once the bullet has been fired it will not speed up due to gravity.

The equation for velocity is v = v0 - at Where v0 is the intial velocity 282 m/s and a is the acceleration of gravity, which is about -9.8 m/s^2. The acceleration of gravity can either be positive or negative depending on the problem. Our equation for this problem would look like this:

v = 282 - 9.8t

This is important because it enables you to determine t or the time it will take to reach the maximum height. The bullet slows down until its velocity is 0. After that the velocity becomes negative and the bullet comes back down. The point where velocity = 0 is where the maximum height occurs.

t = 282/9.8 = 28.7755 seconds

The equation to find height is also necessary to completely solve this problem. The equation to find height is :

h(t) = h0 + v0 t + .5 a t^2

Because you are starting at the ground level, h0 is 0, v0 and a are the same as before

h(t) = 282t - 4.9 t^2

Now you can plug 28.7755 into the equation to solve for the maximum height

h(28.7755) = 282(28.7755) - 4.9 (28.7755)^2 = 4,057.34 m

• Thanks , good looking out ! – Mone Skratt Henry Dec 9 '15 at 14:49

Additionally most practical solution method is kinetic-potential energy equality. If you take air resistance 0, you can easily write: E(pot)=m.g.h=E(kin)=m.v^2/2 Since the starting velocity is known, it can be solved easily.

• You are welcome – Ali Berke Korkmaz Dec 9 '15 at 14:49