Find components of initial velocity given V & H displacement

[-sandro-]

Homework Statement

(this is translated from Italian so it might have some technical mistakes :) )
A target with negligible dimensions is placed at H = 5m from the ground; a vehicle on the ground is
moving at a velocity V = 2m/s (the module) and is getting closer to the target. Consider O the coordinate on the x-axis of the target. When the vehicle is at distance H from O it fires a projectile at the highest path of the trajectory and hits the target. The height of the target is negligible compared to H. Find the x e y components of the velocity (in respect to the ground) and the angle α.

Homework Equations

I used these equations:

1) x = 5= Vix*t
2) y = 5 = Viy*t -1/2*g*t²
3) V_f = Viy - g*t
4) α = arctn(Viy/Vix)

The Attempt at a Solution

Since the velocity when hitting the target at (O,H) is 0 I set the equation 3) to 0 and solved for t getting t = Viy/g then I substituted this value to the equation 2) and solved for Viy getting a value of 9.9m/s, I continued getting a final value of a high angle ...the problem is that from the moment I got Viy I knew something was wrong, how is it possible that the Y component of the velocity V is higher than the module of the velocity? Then I thought that maybe the problem was asking me to find the components of V when hitting the target but how would it? When hitting the target the velocity is 0!

Can you pleasehelp me solve this? I was able to get the solution from a friend done a by a tutor but it does the same thing as me getting that 9.9m/s for Vyx with the difference that the equation 1) is written as x = (Vix+V)*t :| I'm so confused!

Thank you!

EDIT: ok so I think the problem is asking for the velocity components at the time of impact not the initial, and also the final velocity is 0 but it must have some speed when it hits the target but it MUST BE lower than the initial velocity, so that 9.9m/s must be wrong anyways. More confused than before :D

 

[voko]

The given velocity - 2 m/s - is the velocity of the vehicle that fires the projectile, not of the projectile itself. Your result - 10 m/s for the vertical velocity of the projectile - is correct.

 

[-sandro-]

Thank you. I'm still confused though... that value 10m/s that I get is the vertical component of the velocity when it hits the target or of the initial velocity? Being Vix should be the initial but why do we use the coordinates of the target to find the components of initial velocity. I'm not understanding the concept of this.

Plus this is the first time I encounter a problem of this type I thought that firing a projectile at an instant while moving would give me an initial velocity of 2m/s anyway. What kind of motion do I have to study to understand this motion?

What is x = (Vix+V)*t ?

 

[voko]

Thank you. I'm still confused though... that value 10m/s that I get is the vertical component of the velocity when it hits the target or of the initial velocity?

You found this velocity by assuming - correctly - that at the time of the hit the vertical velocity is zero.

Regarding the rest of your questions, observe that you are required to find the components of the projectile's velocity with respect to the ground. The velocity of the vehicle is irrelevant then.

 

[-sandro-]

Ok so that velocity of the vehicle is just there to make my life harder and it's no use?

Basically I got that at the maximum height (where the time t is t/2) the vertical velocity is zero (at that instant the projectile is not moving) exactly where the target is. So the module of |V| of the projectile at t=0 should be 11.07m/s while Vix = 4.95m/s and Viy = 9.9m/s. The resultant angle should be 63.43°.I hope I got it right! Can you confirm? this problem is driving me nuts :P

To find Vix I used x = 5 = Vix*t not x = 5 = (Vix+V)*t as used by the tutor cause I don't understand why he adds that +V being the speed of the vehicle irrelevant like you said!

 

[voko]

Yes, this all looks good.

Regarding the velocity of the vehicle, your description states that you need to find the velocity data with regard to the ground. It may be that you translated this incorrectly, or misunderstood the original problem.

What you can do is solve the problem with respect to the vehicle, too.

 

[-sandro-]

Thank you so much! The translation is correct, the problem does ask to calculate with regard to the ground.

You saved my day ;)