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

• salmayoussef
In summary, the problem involves a mountain climber stranded on a ledge 30 m above the ground and rescuers trying to shoot a projectile with a rope attached to reach the climber. The given information includes the horizontal distance of 50 m, vertical distance of 30 m, initial angle of 55°, and acceleration due to gravity of -9.8 m/s2. The required values are the time and initial velocity of the projectile. The attempted solution involves finding the time using t = dx/Vx = 50/(cos55 * V0) and then using it to solve for the initial velocity using the equation d = V * t - (1/2)(-9.8)(t)2. The resulting
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:
dx = 50 m
dy = 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 = dx/Vx = 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?

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

## 1. What is projectile motion?

Projectile motion is the motion of an object through the air under the influence of gravity. It follows a curved path known as a parabola.

## 2. How do you find the unknown variable (initial velocity) in projectile motion?

In order to find the initial velocity, you need to know the other variables involved in projectile motion: the initial height, the angle of projection, and the range. Using equations of motion and trigonometry, you can solve for the initial velocity.

## 3. What is the formula for finding the initial velocity in projectile motion?

The formula for finding the initial velocity in projectile motion is: v0 = √(gR/2sinθ), where g is the acceleration due to gravity, R is the range, and θ is the angle of projection.

## 4. What is the significance of finding the initial velocity in projectile motion?

The initial velocity is an important variable in projectile motion as it determines the trajectory of the object. It also allows us to make predictions about the motion of the object and calculate other important quantities, such as the maximum height and time of flight.

## 5. Can we use the same method to find the initial velocity for all types of projectile motion?

Yes, the same method can be used to find the initial velocity for all types of projectile motion as long as the object is only under the influence of gravity. However, if there are other forces acting on the object, such as air resistance, the calculations may be more complex.

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