Simple Projectile Motion I'm sure

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SUMMARY

The discussion centers on calculating the time of flight for a projectile launched from a spring-loaded launcher at a 35-degree angle to hit a target 8 meters away. The relevant equations include the horizontal motion equation \(x = x_0 + V_{0x}t\) and the vertical motion equation \(y = y_0 + V_{0y}t - \frac{1}{2}gt^2\). The time of flight is derived using the formula \(T = \frac{2V_0 \sin(35)}{g}\), where \(g\) is the acceleration due to gravity. The solution emphasizes the relationship between horizontal and vertical components of motion to determine the initial velocity \(V_0\).

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  • Understanding of basic kinematics in physics
  • Familiarity with projectile motion equations
  • Knowledge of trigonometric functions, specifically sine and cosine
  • Basic algebra for solving equations
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  • Study the derivation of projectile motion equations
  • Learn how to apply trigonometric functions in physics problems
  • Explore the effects of air resistance on projectile motion
  • Practice solving real-world projectile motion problems using different angles
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Homework Statement


A group of physics students are conducting an experiment in projectile motion. They want to launch a ball into a bucket that is 8 m away from their spring-loaded launcher. They have hypothesized that by setting their launcher to its long-range setting and placing the launcher barrel at a 35 degree angle that they can consistently hit the bucket when they fire the launcher. Ignoring air resistance, calculate the time of flight for the ball in their experiment.


Homework Equations



x=x0+V0xt
Vy=V0y-gt
y=y0+V0yt-1/2gt^2
x=(V0cos(theta))t
y=(V0sin(theta))t-1/2gt^2
Vx=V0cos(theta)0
Vy=V0sin(theta)-gt

The Attempt at a Solution



Not sure but I know this is simple. I am just brain dead right now because I am really sick but I need to get this done for tomorrow. I think you find the time using the y-components...
 
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You know the angle θ. You know that Vox = 8m / T = Vo*Cos35

You also know that VoSinθ is vertical velocity.

From V = Vo - g*T

you know then that time of flight is

VoSin35 - g*T/2 = -VoSin35 or T = 2VoSin35/g

Since T in both equations is equal then you can determine Vo and then you can figure the total time.
 

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