# Projectile Motion Question To Find Unknown Variable (Initial Velocity)

**1. The problem statement, all variables and given/known data**

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/s^{2}

Required:

Δt

V_{0}

**2. Relevant equations**

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

**3. The attempt at a solution**

I tried finding Δt first by using t = d_{x}/V_{x} = 50/(cos55 * V_{0})

After finding the time, I used it an inputed it into the equation and canceled out the V_{0} in the numerator and denominator then I was left with one V which I had to find by rearranging the equation.

30 m = (sin55 * V_{0})(50/(cos55 * V_{0}) – 4.9(50/cos55 * V_{0})^{2}

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

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