Deriving Velocity For Projectiles

In summary, the equation for deriving velocity for projectiles is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. This equation is derived from the basic equation of motion, s = ut + 1/2at^2, by rearranging and solving for v. Its significance lies in its ability to calculate the velocity of a projectile at any given time, making it useful in physics and engineering. It can be used for both horizontal and vertical motion with constant acceleration, and has real-world applications in ballistics, sports, and space exploration.
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jerromyjon
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I have a projectile that can only launch at 30 degrees and a target exactly 100m away at the same elevation on flat ground with 1g (9.8m/s2 meters per second per second?) What velocity without (then with) air resistance would the "muzzle velocity" need to be? (with a droplet shape for resistance)

I can't even figure out how to get started with a minimum mass and velocity to "just make it".
 
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1. What is the equation for deriving velocity for projectiles?

The equation for deriving velocity for projectiles is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

2. How is the equation derived?

The equation is derived using the basic equation of motion, s = ut + 1/2at^2, where s is the displacement. By rearranging this equation and solving for v, we get the equation v = u + at.

3. What is the significance of this equation?

This equation is significant because it allows us to calculate the velocity of a projectile at any given time. It is commonly used in physics and engineering to analyze the motion of objects in free fall or other projectile motion scenarios.

4. Can this equation be used for both horizontal and vertical motion?

Yes, this equation can be used for both horizontal and vertical motion as long as the acceleration is constant. In horizontal motion, the acceleration is usually zero, so the equation simplifies to v = u, where v and u are the final and initial velocities, respectively.

5. What are some real-world applications of this equation?

This equation is commonly used in ballistics, such as calculating the trajectory of a bullet or a projectile launched from a catapult. It is also used in sports, such as calculating the speed of a baseball pitch or a tennis serve. Additionally, this equation is used in space exploration to analyze the motion of spacecraft and satellites.

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