Projectile: Find initial velocity without time

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SUMMARY

The discussion focuses on calculating the initial velocity (v0) of snow discharged at a 40-degree angle without knowing the time variable. The solution involves using the equations for horizontal and vertical motion: L = v0 t cos(θ) and Δy = v0 t sin(θ) - (1/2) g t². By solving the first equation for time (t) and substituting it into the second equation, the initial velocity can be determined. The final calculated initial speed is 6.98 m/s, confirming the accuracy of the approach.

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Homework Statement


Knowing that snow is discharged at an angle of 40 degrees, determine the initial speed, v0 of the snow at A. Answer: 6.98 m/s

Homework Equations



snow%20thrower.jpg


projectile.jpg


The Attempt at a Solution



I have found the x and y velocity and position formulas. Now since I don't know time, should I solve both position equations for time (t) and set them equal to each other to get my only unknown, vi? The quadratic equation for time in the y-dir seems a bit hectic. Is there an easier way to go about trying to find vi?
 
Last edited:
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Start with
L = v0 t cosθ
Δy = v0 t sinθ - (1/2) g t2

Solve the first equation for t and replace in second equation. Solve the ensuing equation for v0.
 
kuruman said:
Start with
L = v0 t cosθ
Δy = v0 t sinθ - (1/2) g t2

Solve the first equation for t and replace in second equation. Solve the ensuing equation for v0.

I believe this is what you had in mind. The answer matches the professor's answer. Thanks again kuruman!

projectile%20final.jpg
 

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