Kinematics in Two or Three Dimensions

AI Thread Summary
A baseball is hit at an initial speed of 29 m/s at a 55° angle, while an outfielder is positioned 85 m away at a horizontal angle of 22° from the batter's line of sight. The problem requires calculating the speed and direction the outfielder must run to catch the ball at the same height it was struck. Participants in the discussion express difficulty in solving the problem and seek guidance on the specific steps to take. The conversation highlights the need for a clear understanding of kinematic equations and vector components in two or three dimensions. Effective problem-solving strategies are essential for finding the solution.
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Homework Statement


At t = 0 a batter hits a baseball with an initial speed of 29 m/s at a 55° angle to the horizontal. An outfilder is 85 m from the batter at t = 0 and, as seen from home plate, the line of sight to the outfilder makes a horizontal angle of 22° with the plane in which the ball moves. What speed and direction must the fielder take to catch the ball at the same height from which it was struck? Give the angle with respect to the outfilder's line of sight to home plate.

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Homework Equations



The Attempt at a Solution

 
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can you find the answer?i have the same problem.
 
Where are you getting stuck in solving this?
 
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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