# Projectile Launched at an angle problem.

• KingHenry
In summary: For the second part, you can use the same equation but this time solve for t and set the final x position equal to the distance between the cannon and the projectile's landing spot. Then solve for t and plug it back into the equation to find the horizontal distance from the cannon. In summary, using the equation x - x_0 = v_0cos(\theta)t + \frac{1}{2}at^2, the horizontal range observed by a person standing on the ground when a cannon fires a projectile from a
KingHenry

## Homework Statement

A spring-loaded cannon aimed at 47 degrees above the horizontal is on the last car of a long train of flat cars. The train has an initial velocity of 54.3 km/h. At the moment the train begins to accelerate forward at 0.325 m/s2 , the cannon fires a projectile at 180 m/s. The cannon points in the direction that the train is moving.
a.) What is the horizontal range observed by a person standing on the ground?
b.) How far on the train from the cannon does the projectile land? Neglect air resistance

## Homework Equations

x=Vi*t+ 1/2a(t)^2

## The Attempt at a Solution

I know that x component is 180cos 47 and y component is 180sin 47. Not sure where to go from here

I'm also in this section of my Physics class but I can be of some help.

I found this formula from my book: $$x - x_0 = v_0cos(\theta)t + \frac{1}{2}at^2$$. So I THINK that for the first part, you have to somehow find the t and get the distance.

EDIT: AS I LOOKED AROUND THE SECTION, THERE IS A SPECIAL FORMULA FOR THE HORIZONTAL RANGE

The formula is: $$R = \frac{v_0^2}{g}sin(2\theta_0)$$
Plugging into the formula should give you the horizontal range.
PS. What book are you using, if you are using a book at all?

Last edited:
The book I am using is holt physics

Well, you should be able to get the horizontal range, I'm not sure how to do the second part though, I mean I have an idea but I'm not sure if it is correct at all.

you should first scetch yourself a quick visual of what the question is asking and then draw an x l y chart so that you can separate your x and y variables. this makes it much easier to see what you have and what you need to find in terms of x and y
also try using the equaton
$$x - x_0 = v_0cos(\theta)t + \frac{1}{2}at^2$$

## 1. How do I calculate the initial velocity of a projectile launched at an angle?

To calculate the initial velocity, you will need to know the angle at which the projectile is launched, the initial height of the projectile, and the range of the projectile. You can use the formula v0 = √(gR / sin2θ), where v0 is the initial velocity, g is the acceleration due to gravity, R is the range, and θ is the launch angle.

## 2. What is the maximum height reached by a projectile launched at an angle?

The maximum height reached by a projectile launched at an angle is determined by the initial velocity and the launch angle. The formula for calculating maximum height is hmax = (v0sinθ)^2 / 2g, where hmax is the maximum height, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

## 3. How do I determine the time of flight for a projectile launched at an angle?

To determine the time of flight, you can use the formula t = (2v0sinθ) / g, where t is the time of flight, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity. This formula assumes that the initial and final heights are the same.

## 4. What is the range of a projectile launched at an angle?

The range of a projectile launched at an angle is the horizontal distance traveled by the projectile. The formula for calculating range is R = (v0^2 sin2θ) / g, where R is the range, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

## 5. How do I take air resistance into account when solving a projectile launched at an angle problem?

To take air resistance into account, you will need to use more complex equations and consider factors such as air density, drag coefficient, and cross-sectional area of the projectile. Alternatively, you can use a computer program or simulation that already accounts for air resistance in its calculations.

• Introductory Physics Homework Help
Replies
7
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
15
Views
1K
• Introductory Physics Homework Help
Replies
36
Views
3K
• Introductory Physics Homework Help
Replies
4
Views
964
• Introductory Physics Homework Help
Replies
3
Views
3K
• Introductory Physics Homework Help
Replies
15
Views
8K
• Introductory Physics Homework Help
Replies
9
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
2K