# Firing a projectile, max height + flight time

1. Homework Statement
A projectile is fired with an initial speed of 65.2 m/s at an anmgle of 34.4 degrees above the horizontal on a long flat firing range.
Determine the max heigh reached by the prkectile, the total time in the air and the total horizontal distance covered and the velocity of the projectile 1.50 seconds after firing.

2. Homework Equations and 3. The Attempt at a Solution
I am going to check the first parts now, and then continue once I am sure I am going in the right direction.

Vxo = vocos 34.5 = 65.2/0.824 = 79.1 m/s
Vyo = vosin34.5 = 65.2/0.566=115 m/s

t=vyo/g=11.7 seconds.
y=Vyot - 1/2gt^2= 675 meters maximum height.

And

y=yo + vyot - 1/2 gt^2
0 = 0 + 115t - 1/2 x 9.80 x t^2
t = 0 at initial point
t= 2 (115)/9.80 = 23.5 seonds.

Thanks!

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Actually here's the third part
Range:
x = 0. ax=0, vxo= 79.1 m/s and 11.7x2 = 23.4 which is the total time for the whole "trip".
x= 79.1 x 23.4 = 1850.94 meters

For the velocity after 1.50 seconds, I have no idea how to proceed... Some help would be greatly appreciated. Thanks!

Do I use the same equation as in the previous part:
x= 79.1 x 23.4 = 1850.94 meters
but replace 23.4 by 1.50 seconds
=> 79.1 x 1.5 = 118.7 meters ?
How about the significant figures throughout the exercise?

Thanks!

HallsofIvy
Homework Helper
1. Homework Statement
A projectile is fired with an initial speed of 65.2 m/s at an anmgle of 34.4 degrees above the horizontal on a long flat firing range.
Determine the max heigh reached by the prkectile, the total time in the air and the total horizontal distance covered and the velocity of the projectile 1.50 seconds after firing.

2. Homework Equations and 3. The Attempt at a Solution
I am going to check the first parts now, and then continue once I am sure I am going in the right direction.

Vxo = vocos 34.5 = 65.2/0.824 = 79.1 m/s
Vyo = vosin34.5 = 65.2/0.566=115 m/s
?? You say Vxo= vocos 34.5 but then you DIVIDE by cos 34.5? Same for Vyo. Surely the x and y components of speed can't be greater than the speed itself!

t=vyo/g=11.7 seconds.
y=Vyot - 1/2gt^2= 675 meters maximum height.

And

y=yo + vyot - 1/2 gt^2
0 = 0 + 115t - 1/2 x 9.80 x t^2
t = 0 at initial point
t= 2 (115)/9.80 = 23.5 seonds.

Thanks!
Your values for vxo and vyo are wrong. Recalculate them- multiply by the trig functions- and recalculate the rest.

Actually here's the third part
Range:
x = 0. ax=0, vxo= 79.1 m/s and 11.7x2 = 23.4 which is the total time for the whole "trip".
x= 79.1 x 23.4 = 1850.94 meters
Again, your value for vxo is wrong. Recalculate.

For the velocity after 1.50 seconds, I have no idea how to proceed... Some help would be greatly appreciated. Thanks!
Do I use the same equation as in the previous part:
x= 79.1 x 23.4 = 1850.94 meters
but replace 23.4 by 1.50 seconds
=> 79.1 x 1.5 = 118.7 meters ?
How about the significant figures throughout the exercise?

Thanks!
"x" is not the velocity, it's horizomtal distance. The velocity is the <vx, vy> vector. Since, as you said before, there is no horizontal acceleration, vx is just vxo. vy is, of course, vyo- gt.

cristo
Staff Emeritus
1. Homework Statement
A projectile is fired with an initial speed of 65.2 m/s at an anmgle of 34.4 degrees above the horizontal on a long flat firing range.
Determine the max heigh reached by the prkectile, the total time in the air and the total horizontal distance covered and the velocity of the projectile 1.50 seconds after firing.

2. Homework Equations and 3. The Attempt at a Solution
I am going to check the first parts now, and then continue once I am sure I am going in the right direction.

Vxo = vocos 34.5 = 65.2/0.824 = 79.1 m/s
Vyo = vosin34.5 = 65.2/0.566=115 m/s
Check these components: Vx0=V0*cos34.5; here you've divided!

(plus you've put 34.4 in the first line of the question!)

!!! How brainless.

Well, here is the correction:
Same but multiplying instead gives us 5.15 m/s and 36.9 m/s.
t= 3.77 seconds.
Then for the distance following y=Vyot - 1/2gt^2= 69.5 meters maximum height.

Then we have
y=yo + vyot - 1/2 gt^2
0 = 0 + 36.9t - 1/2 x 9.80 x t^2
t = 0 at initial point
t= 2 (36.9)/9.80 = 7.5 seconds.

And finally for the range:
The time was 3.77 => 3.77 x 2 = 7.54 seconds for the whole trip
x= 5.15 x 7.54 = 38.8 meters

cristo
Staff Emeritus
!!! How brainless.

Well, here is the correction:
Same but multiplying instead gives us 5.15 m/s and 36.9 m/s.
t= 3.77 seconds.
Then for the distance following y=Vyot - 1/2gt^2= 69.5 meters maximum height.
Check the x component of the initial velocity again. Other than that, I've not checked your arithmetic, but your method is correct.

Then we have
y=yo + vyot - 1/2 gt^2
0 = 0 + 36.9t - 1/2 x 9.80 x t^2
t = 0 at initial point
t= 2 (36.9)/9.80 = 7.5 seconds.
Correct

And finally for the range:
The time was 3.77 => 3.77 x 2 = 7.54 seconds for the whole trip
x= 5.15 x 7.54 = 38.8 meters
x component of initial velocity is incorrect (as above)

For the last question, do I replace 7.54 by 1.5 seconds to find the distance after 1.5 seconds?
Yes, but don't you want the velocity after 1.5 seconds?

Last edited:
(plus you've put 34.4 in the first line of the question!)
Oops... It is 34.5 degrees... =/

cristo
Staff Emeritus
Oops... It is 34.5 degrees... =/
OK, I thought as much, and that that was a typo. Did you see my above post re a mistake in the x component of the initial velocity?

Yes, thank you! It did look small. I can't believe I am making so many mistakes...

Actually, yes I need the velocity not the distance.
Do I use:
vyo- gt = the velocity
=> = 36.9m/s - 9.80 m/s^2 x 1.50 seconds = 14.85 m/s ?

I think I spent too much time on this exercise, nothing is making sense anymore and I am mixing up my numbers...

cristo
Staff Emeritus
Actually, yes I need the velocity not the distance.
Do I use:
vyo- gt = the velocity
=> = 36.9m/s - 9.80 m/s^2 x 1.50 seconds = 14.85 m/s ?

I think I spent too much time on this exercise, nothing is making sense anymore and I am mixing up my numbers...
That gives you the y component of the velocity at the time t=1.5. Then calculate the x component of the velocity at this point.

To calculate the velocity at this point you need to find (a) the speed (i.e. magnitude of the velocity) at this point, and (b) the angle the velocity makes to the horizontal.

So, you can write the velocity v at this point to be v=(vcosθ, vsinθ), and you need to solve equations for v and θ