# Find Initial Velocity of a projectile given flight time and angle

• Asem
In summary, the conversation discusses projectile motion and the equations involved in calculating the velocity and displacement of a projectile. The speaker asks about the symmetry of vertical motion and the final velocity when a projectile is launched from ground level. The expert responds that while the vertical motion is symmetric, the final velocity will have the same magnitude but opposite direction as the initial velocity when the projectile returns to the same level. The expert also gives a helpful tip to start with the equations for vertical motion when solving projectile problems.

#### Asem

Homework Statement
A player kicks a football at an angle of 40 degrees to the ground if it hits the ground after 2 seconds.Then what is the initial velocity
Relevant Equations
None
Vix=Vcosθ
Vix=0.76604*V
Xf=Vixt
Xf=0.77604V*2
V=Xf/1.55208

Is there a question you wish to ask?

What can you determine by considering the vertical component of motion?

Range, but to find that I need Vix

What @TSny suggests, and I agree, is that perhaps you should consider the motion in the vertical direction instead of in the horizontal direction.

can I say final velocity is equal to zero?

If I can
Vf=Viy+at
Viy=-at
Viy=-(-9.8*2)
Viy=19.6

Viy=Vsin
19.6=Vsin40
V=30.5

The only problem is this is apparently wrong as there is no choice of answer that is 30.5

At t= 2 s, the projectile is just starting to impact the ground. The y component of velocity is not zero at t = 2s.

Asem
Asem said:
can I say final velocity is equal to zero?
No. The projectile is always moving and its velocity is never zero. The equations that you have are valid from the time it starts moving until just before the projectile hits the ground.
Hint: What happens when the projectile reaches maximum height? What is zero then?

Asem
Vf=0, when t=1s
Vf=Viy+at
Viy=9.8*1

Viy=Visin
9.8=Visin(40)
Vi=15.2
Thank you, sir

Asem said:
Vf=0, when t=1s
Vf=Viy+at
Viy=9.8*1

Viy=Visin
9.8=Visin(40)
Vi=15.2
Thank you, sir
Good! Remember this for future reference: In projectile motion problems that give you the time of flight (or ask you to find the time of flight), always start with the equations for the vertical motion. That's because the value of g is what determines how long a projectile stays in the air.

Asem
I just have one more question; Vertical motion is symmetric in projectile right? So, is Initial velocity = Final velocity? If projectile is launched from ground level I mean.

jbriggs444
Asem said:
I just have one more question; Vertical motion is symmetric in projectile right? So, is Initial velocity = Final velocity? If projectile is launched from ground level I mean.
Yes.

As long as we are ignoring air resistance and, as you have already specified, that launch and landing are at the same height.

Edit: as @kuruman points out, the vertical velocity component will be inverted. So the two velocities will be mirror symmetric rather than strictly equal.

Last edited:
kuruman
Asem said:
I just have one more question; Vertical motion is symmetric in projectile right? So, is Initial velocity = Final velocity? If projectile is launched from ground level I mean.
No. When the projectile returns to the same level, the final speed is the same as the initial speed. The horizontal component of the velocity is the same while the final vertical component has the same magnitude but opposite direction from the initial component.

jbriggs444