Using quadratic formula to find time [projectile motion]

AI Thread Summary
To find the time of flight for a projectile launched at an angle, the discussion emphasizes using the Y components of motion. The relevant equation is ΔY = Viyt + 1/2ayt², which can be rearranged into a quadratic formula. The user initially struggles with the equation -4.9t² + 0 + 0.96 = 0, mistakenly believing it to be incorrect due to a zero variable. Ultimately, the solution is to solve the quadratic equation for t, highlighting the simplicity of the approach. The discussion illustrates the importance of correctly applying the quadratic formula in projectile motion problems.
camcognito
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1. Homework Statement
I'm doing lab, and to start we have to find ΔX of a projectile launched an angle. The first step for us is to find time, and to make it easier our teacher recommended us to first set the angle to zero, and find time like that.

I don't have enough X information to find time yet, so I have to use the Y components I think

X
ΔX= .153 M
Φ = 0°
Y
AY = 9.8m/s2
ΔY = -.96 M.
Φ = 0°
Viy = 0 ?

Homework Equations


I'm supposed to take the equation ΔY = Viyt + 1/2ayt2 and make it into quadratic formula. For some reason t = √2ΔY/AY won't work and we're supposed to use quadratic formula

The Attempt at a Solution


[/B]
Since I'm launching the projectile from 0°, I thought the Viy would equal 0. However, when I try to plug that into the quadratic formula, there's a 0 for one of the variables and it doesn't work.

I'm getting -4.9t2 + 0 + .96 = 0; I think I'm doing something wrong in the middle but I'm not sure what to fix.
 
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camcognito said:
1. Homework Statement
I'm doing lab, and to start we have to find ΔX of a projectile launched an angle. The first step for us is to find time, and to make it easier our teacher recommended us to first set the angle to zero, and find time like that.

I don't have enough X information to find time yet, so I have to use the Y components I think

X
ΔX= .153 M
Φ = 0°
Y
AY = 9.8m/s2
ΔY = -.96 M.
Φ = 0°
Viy = 0 ?

Homework Equations


I'm supposed to take the equation ΔY = Viyt + 1/2ayt2 and make it into quadratic formula. For some reason t = √2ΔY/AY won't work and we're supposed to use quadratic formula

The Attempt at a Solution


[/B]
Since I'm launching the projectile from 0°, I thought the Viy would equal 0. However, when I try to plug that into the quadratic formula, there's a 0 for one of the variables and it doesn't work.

I'm getting -4.9t2 + 0 + .96 = 0; I think I'm doing something wrong in the middle but I'm not sure what to fix.

The equation -4.9t2 + 0 + .96 = 0 is correct, just solve it for t.
 
ehild said:
The equation -4.9t2 + 0 + .96 = 0 is correct, just solve it for t.
Wow... it was that simple. Thanks, I've been overthinking a lot of equations recently
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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