Calculating Range: Zero Air Resistance, Baseball

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To calculate the range and maximum height of a baseball hit at an angle with zero air resistance, it's essential to analyze the motion in both horizontal and vertical axes. The range is measured along the horizontal axis, where the only force acting is the initial velocity. In the vertical axis, gravity is the primary force affecting the ball's motion. Formulating the equations for acceleration and displacement involves using kinematic equations, specifically considering the initial velocity and the angle of projection. Understanding these principles will lead to the correct calculations for range and maximum height.
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Homework Statement


zero air resistance. baseball player hits ball at angle theta above the horizontal at a initial velocity of "z" m/s...how does one calculate range and max height given the fact that the ball lands several metres above where it was originally hit?



Homework Equations


d= vit + 1/2at^2 i think?


The Attempt at a Solution


i need a hint or two please?
 
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three hints:

-in which axis is "range" measured?
-what forces do you have acting in this axis?
-based on these forces, formulate your acceleration and displacement equations.
 
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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