Find Initial Velocity given angle, distance, height launched from.

AI Thread Summary
To find the initial velocity of a nerf gun fired from a height of 0.98 meters at a 15-degree angle over a distance of 7.86 meters, the equations of motion are utilized. The horizontal motion equation is simplified to express time in terms of initial velocity, leading to the equation t = 7.86/(vocos15). For vertical motion, the equation incorporates the initial vertical velocity and gravitational acceleration, resulting in -.98 = voy*t - 4.9t^2. Substituting the expression for time from the horizontal motion into the vertical equation allows for solving the two equations simultaneously. This method effectively leads to determining both the initial velocity and its horizontal and vertical components.
mhsphysics10
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1. A nerf gun in a vacuum is fired from .98 meters at an angle of 15degrees, going 7.86m. Find the initial velocity of the gun, then find the horizontal and vertical components of the initial velocity.

Knowns
g=-9.8m/s2
yo=.98m
xo=0m
y=o ( the final height of the dart is 0)
x=7.86m
θ=11 degrees



Homework Equations


x=xo+vot
y=yo+vot+.5gt2
vox=vocosθ
voy=vosinθ

The Attempt at a Solution


So first i simplified the x equation down to get time on one side to get
(x-xo)/(vocos11)=t
Then i plugged in the numbers to get
{7.86/(vocos11)}=t

Then i plugged in the parts for the y equation,
-.98=voyt+-4.9t2
Now what do i do? do take out a t and plug in the x equation?
 
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Why not substitute in v_0* sin (theta) = v_0y. Then you have two equations and two unknowns and from that everything else is easy to find!
 
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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