Finding initial and final velocities of projectile

[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
vfy^2 = viy^2 + 2ad

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

vfy^2 = viy^2 + 2ady
= (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.

 

[anathema]

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.