Calculating Vertical Height & Speed of Bullet Fired Upwards

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Homework Help Overview

The problem involves calculating the vertical height and speed of a bullet fired upwards, taking into account air resistance that is proportional to the speed. The scenario includes specific parameters such as initial speed, mass of the bullet, and gravitational acceleration.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of Newton's second law and the effects of air resistance on the bullet's motion. There is uncertainty about how to modify the equations for the upward motion of the bullet compared to free fall.

Discussion Status

Some participants have provided guidance on the use of Newton's second law and the importance of considering the direction of forces acting on the bullet. There is an ongoing exploration of the correct formulation of the equations needed to solve the problem.

Contextual Notes

Participants are navigating the complexities introduced by air resistance and the need for integration in their calculations. The original poster expresses uncertainty about how to initiate the problem-solving process.

espenth
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A bullet fired vertically upwards with a beginning speed 70 m / s. In this task, we shall assume that the sphere is exposed to air resistance is proportional to the speed, and given by. Proportionality constant k = 1.6 * 10 ^ -2 kg / s and the bullets mass m = 0.100 kg. We expect that the acceleration due to gravity is constant g = 9.81 m/s2.

a) Calculate how high the ball is coming, and how long it takes to peak.

b) What speed is the bullet when it comes back to the starting point, and how long does it take from the vertex to the starting point? What is the acceleration, then?

I guess I have to use integration on the air resistance, but I don't know how to start on this question. Anyone got a sugestion?
 
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Perhaps you start with Newton's second law?

ehild
 
I know about Newtons law..

In free fall, with air resistance, the equation is something like:

m*g - k*v = m*dV/dT.

But this is for free fall, I guess the one I need is a little bit different?
 
It is almost the same, but take care of the signs. If the bullet goes upward, both gravity and air resistance point downward.

ehild
 

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