Help Solving air drag projectile problem

In summary, the conversation is about finding the formula for the time of a projectile influenced by air drag, specifically when launched from either y=0 or some height. The formula given is (48/.5)(1-^e-.5t)(sin 45) + (9.8/.25)(1-(.5t) - e^-.5t) = 0 and the conversation goes on to discuss how to solve for t using logarithms. The conversation also mentions a previous thread that was not receiving enough attention.
  • #1
Matt Jacques
81
0
Since my other thread is lacking attention, perhaps it is more suitable here:

I inserted some fixed constants and multiplied out

(48/.5)(1-^e-.5t)(sin 45) + (9.8/.25)(1-(.5t) - e^-.5t) = 0

(96 - 96e^-.5t)(sin 45) + 39.2(1-(.5t)-e^-.5t) = 0

67.88 - 67.88^e-.5t + 39.2 - 19.6t - 19.6e^-.5 = 0

107.2 - 87.48e^-.5t - 19.6t = 0

107.2 - 19.6t = 87.48^e-.5t

log(107.2 - 19.6t) = log(87.48^e-.5t)

log107.2 - log19.6t = -.5tLog(87.48)

2.030194 - log19.6t = -.5t(1.94198)

1.045463 - log19.6t = -.5t

-(1.045463 - log19.6t = -.5t)

-1.045463 + log19.6t = .5t

log19.6t = .5t + 1.045463

10^(.5t + 1.045463) = 19.6t

This is where I am stuck.
 
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  • #2
Matt,

Could you post the original problem, or a link to your other thread? I don't see what you're trying to do with this.
 
  • #3

FAQ: Help Solving air drag projectile problem

What is air drag and how does it affect projectile motion?

Air drag, also known as air resistance, is the force exerted by air on an object as it moves through the air. This force opposes the motion of the object and can cause it to slow down or change direction. In projectile motion, air drag can decrease the distance traveled and alter the trajectory of the projectile.

How do you calculate air drag in a projectile problem?

The calculation of air drag in a projectile problem involves using the formula Fd = 0.5 * ρ * v^2 * A * Cd, where Fd is the drag force, ρ is the density of air, v is the velocity of the object, A is the cross-sectional area of the object, and Cd is the drag coefficient. This formula takes into account the speed, size, and shape of the object, as well as the density of air, to determine the drag force acting on the projectile.

How can air drag be minimized in a projectile problem?

Air drag can be minimized in a projectile problem by reducing the surface area of the object, increasing the velocity, and using a streamlined shape. This can be achieved by using a pointed or streamlined object, such as a bullet, and increasing the initial velocity of the object. Additionally, reducing the density of the air by launching the projectile at higher altitudes can also decrease the effects of air drag.

How does air drag affect the range of a projectile?

Air drag can significantly affect the range of a projectile. As the projectile travels through the air, it experiences a drag force that decreases its speed and alters its trajectory. This results in a shorter range compared to a similar object without air drag. The amount of air drag depends on the velocity, size, and shape of the object, as well as the density of the air.

How can you account for air drag in a projectile problem?

To account for air drag in a projectile problem, you can use the above-mentioned formula Fd = 0.5 * ρ * v^2 * A * Cd to determine the drag force acting on the object. This force can then be incorporated into the equations of motion to calculate the trajectory and range of the projectile. Alternatively, you can use computer simulations or conduct experiments to measure the effects of air drag on the projectile and adjust your calculations accordingly.

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