# Finding initial and final velocities of projectile

• fiftybirds
In summary, final velocity for a rocket launch must take into account the launch angle and angle to the apex, and is calculated using vector addition of the horizontal and vertical components of the initial velocity. The final horizontal velocity may not be the same as the initial horizontal velocity due to potential changes in horizontal acceleration.
fiftybirds

## Homework Statement

I had to calculate initial and final velocities for a rocket launch. Data are as follows:

horiz displacement = 17.5m
time = 3.5 s
launch angle = 40 deg
angle to apex from 20m = 11 deg
net vertical displacement = 0

## Homework Equations

I used the following equations:

d = vit + (a[t^2])/2

## The Attempt at a Solution

calculations for initial velocity

horizontal

dx = vixt + (aav[t^2])/2
17.5 m = 3.5s(vix) + (-9.81 m/s^2[3.5s^2])/2
77.6 m/3.5 s = vix
22.2 m/s = vix

vertical
0m = viy(3.5s) + (-9.81 m/s^2[3.5s^2])/2
60.1 m/3.5s = viy
viy = 17.2 m/s

then final velocity

= (17.2 m/s)^2 + 2 (-9.81m/s^2)(0)
= -17.2 m/s ?

I used d = vit -(a[t^2])/2 to calculate this again and got the same answer.

It doesn't seem right that the final velocity would be the same magnitude as the initial velocity... is this answer correct? It also doesn't make sense that we had to measure the launch angle and angle to the apex if they aren't required to solve the problem

Also, since horizontal velocity is constant, wouldn't the final horizontal velocity be the same as the initial horizontal velocity?

Thanks.

Hello,

Your initial calculations for the horizontal and vertical components of the initial velocity look correct. However, your calculation for the final velocity does not seem to take into account the launch angle and angle to the apex. These angles are important because they affect the overall trajectory of the rocket and therefore the final velocity.

To calculate the final velocity, you will need to use vector addition to combine the horizontal and vertical components of the initial velocity. This will give you the final velocity at the apex of the rocket's trajectory. You can then use this final velocity to calculate the final horizontal and vertical velocities, taking into account the angle to the apex and launch angle.

Additionally, it is important to note that the final horizontal velocity will not necessarily be the same as the initial horizontal velocity, as the rocket may experience changes in horizontal acceleration during its trajectory.

I hope this helps. Let me know if you have any further questions.

## What is a projectile?

A projectile is any object that is launched into the air and moves under the force of gravity. Examples of projectiles include a baseball thrown by a pitcher, a bullet fired from a gun, or a stone thrown by a person.

## How do you find the initial velocity of a projectile?

The initial velocity of a projectile can be calculated by using the formula v0 = Vo = v cosθ, where v0 is the initial velocity, v is the magnitude of the velocity, and θ is the angle of launch. This formula takes into account both the speed and direction of the projectile at the moment it is launched.

## What is the final velocity of a projectile?

The final velocity of a projectile is the velocity at the moment right before it hits the ground or any other target. It can be calculated using the formula v = √(v02 + 2gh), where v0 is the initial velocity, g is the acceleration due to gravity (9.8 m/s2), and h is the height of the projectile.

## How does air resistance affect the initial and final velocities of a projectile?

Air resistance can have a significant impact on the initial and final velocities of a projectile. It can reduce the initial velocity and change the direction of the projectile, as well as decrease the final velocity due to the force of drag acting on the object as it moves through the air.

## Can the initial and final velocities of a projectile be the same?

Yes, the initial and final velocities of a projectile can be the same if the projectile is launched at a 45-degree angle with no air resistance. This is because the horizontal and vertical components of the projectile's velocity will be equal, resulting in the same initial and final velocities.

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