# Projectile motion boat gun problem

• jesusu2
In summary, the problem involves a speedy destroyer firing a projectile at an angle to the horizontal. The projectile travels 23 500 m in 135 seconds and the goal is to find its initial velocity. To solve this, the problem can be split into three parts: up, down, and horizontal. After 135 seconds, the shell spends 67.5 seconds going up and 67.5 seconds coming back down. Using this information, the vertical and horizontal components of the initial velocity can be calculated, and then solved using Pythagoras and trigonometry. Alternatively, a calculator can be used to convert the rectangular coordinates to polar coordinates.

## Homework Statement

A speedy destroyer’s 5 inch gun fires a projectile at some angle to the horizontal. If the thing travels a distance of 23 500 m in 135 s, what was the projectile’s initial velocity?

## Homework Equations

v=vi+at
v^2=vi^2+2a(s) s=displacement
s=vi*t+.5at^2

## The Attempt at a Solution

Hello, I really don't know where to start, since I don't have an angle. I've made a diagram and split into 3 parts, up, down, and horizontal. How do I progress through this problem!?

jesusu2 said:

## Homework Statement

A speedy destroyer’s 5 inch gun fires a projectile at some angle to the horizontal. If the thing travels a distance of 23 500 m in 135 s, what was the projectile’s initial velocity?

## Homework Equations

v=vi+at
v^2=vi^2+2a(s) s=displacement
s=vi*t+.5at^2

## The Attempt at a Solution

Hello, I really don't know where to start, since I don't have an angle. I've made a diagram and split into 3 parts, up, down, and horizontal. How do I progress through this problem!?

Since this was a destroyer, the shell was fired from sea level, and lands at sea level so at least it lands at the same height from which it started.

The shell got to its target after 135s. That means it spent 67.5 seconds going up, then another 67.5 seconds coming back down.
For something to do that, you can calculate the vertical component of the initial velocity. [ie how fast is an object traveling if it falls for 67.5 seconds]

It landed 23 500m away after 135 seconds, so you can work out its horizontal velocity component.

One you have those two it is off to Pythagoras [and trigonometry if you also want the angle].
Note: you can use Rectangular-to-Polar co-ordinate conversions on you calculator if you are clever enough.

## 1. What is projectile motion and how does it relate to a boat gun problem?

Projectile motion is the motion of an object that is launched into the air and moves under the influence of gravity. In a boat gun problem, the projectile is the bullet or projectile fired from the gun, and the boat is the object that is moving.

## 2. How is the velocity of the boat gun determined in a projectile motion problem?

The velocity of the boat gun can be determined by using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity, and t is the time the projectile is in the air.

## 3. What factors affect the trajectory of the bullet in a projectile motion boat gun problem?

The factors that affect the trajectory of the bullet include the initial velocity of the bullet, the angle at which it is fired, the air resistance, and the gravity. These factors can be manipulated to achieve the desired trajectory.

## 4. How do you calculate the range of a projectile in a boat gun problem?

The range of a projectile can be calculated using the equation R = (u^2sin2θ)/g, where R is the range, u is the initial velocity, θ is the angle of elevation, and g is the acceleration due to gravity. This equation takes into account the horizontal and vertical components of the projectile's motion.

## 5. What is the significance of understanding projectile motion in a boat gun problem?

Understanding projectile motion in a boat gun problem is important for accurately aiming and hitting a target. It also allows for predicting the trajectory of the bullet and making any necessary adjustments to achieve the desired results. Additionally, understanding projectile motion is essential in many other fields of science and engineering, such as ballistics and space exploration.