Projectile Motion without Initial Velocity

AI Thread Summary
A projectile is launched at a 50° angle and lands after 12 seconds, prompting calculations for its maximum height and range. The main challenge is determining the initial velocity (Vo), which is essential for solving the problem. A relevant formula is identified: V_y = V_o * Sin(θ) - gt, where V_y equals zero at the peak height. By finding the time when V_y equals zero, one can derive Vo using trigonometric relationships. This approach enables the calculation of both the maximum height and range of the projectile.
PerryKid
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Projectile Motion without Initial Velocity (Only time and angle given)

Homework Statement



A projectile is launched at an angle of 50° above the horizontal and it hits the ground in 12 seconds.

a. Calculate the maximum height of the projectile.
b. Find the range of the projectile.

Homework Equations



H_{max}=\frac{V_{o}^{2}+sin^{2}\theta}{g}

R=V_{o}\sqrt{\frac{2H}{g}}

The Attempt at a Solution



I don't know where to start. I can't solve without Vo and I am missing Vo.
 
Last edited:
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Can you not use a standard kinematic equation to get vy0?
 
I need [STRIKE]Vo to find height and range, not Vyo[/STRIKE]

EDIT: I found a formula to help me solve it all! :approve:

V_{y}=V_{o}Sin(\theta)-gt

V_{y}=0
 
But if you can find vy0, then you can find v0 with some simple trig.
 
PerryKid said:
EDIT: I found a formula to help me solve it all! :approve:

V_{y}=V_{o}Sin(\theta)-gt

V_{y}=0

That will work. At what t will vy = 0?
 
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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