Projectile Motion Question To Find Unknown Variable (Initial Velocity)

[salmayoussef]

Hey all! I've tried solving this problem every way I could think of and I wanted to see if I'm doing this even remotely right. Mind helping me out?

Homework Statement

Problem: A mountain climber is stranded on a ledge 30 m above the ground. Rescuers on the ground want to shoot a projectile to him with a rope attached it. If the projectile is directed upward at an initial angle of 55° from a horiontal distance of 50 m, derermine the intial speed the projectile must have in order to land on the ledge.

Given:
d_x = 50 m
d_y = 30 m
θ = 55°
g = -9.8 m/s²

Required:
Δt
V₀

Homework Equations

Not sure if I used the proper equation but: d = V * t - (1/2)(-9.8)(t)²

The Attempt at a Solution

I tried finding Δt first by using t = d_x/V_x = 50/(cos55 * V₀)

After finding the time, I used it an inputed it into the equation and canceled out the V₀ in the numerator and denominator then I was left with one V which I had to find by rearranging the equation.

30 m = (sin55 * V₀)(50/(cos55 * V₀) - 4.9(50/cos55 * V₀)²

After rearranging it, I ended up with 30.06 m/s as the initial velocity. Am I using the right equation?

 

[CWatters]

I haven't checked your working but the approach looks correct.