Projectile: Find initial velocity without time

[JJBladester]

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

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, v_i? The quadratic equation for time in the y-dir seems a bit hectic. Is there an easier way to go about trying to find v_i?

 

[kuruman]

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.

 

[JJBladester]

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!