Projectile Problem Help: Find Maximum Distance and Collision Point - g=10m/s2

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To determine the maximum distance from the cliff where the ship's gun can hit an object at the top, the projectile motion equations are applied, considering the gun's velocity of 110 m/s and gravity at 10 m/s². The calculations reveal that the maximum horizontal distance is influenced by the height of the cliff, which is 105 m. For the second scenario involving two towers, the objects are thrown with specified velocities and angles, leading to a collision in mid-air. By using the equations of motion and eliminating time, the distance 'd' between the towers and the ground impact position of the combined objects can be calculated. The discussion emphasizes the application of kinematic equations to solve projectile motion problems effectively.
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1. A ship is approaching a cliff of height 105m above sea level. gun fited on ship can fire shots with 110m/s. Find the maximum distance frm the foot of cliff from where the gun can hit an object on the top of cliff. g=10m/s2

2. 2towers AB and CD are situated a distance 'd' apart. AB is 20m high and CD is 30 m high frm ground. an object of mass 'm' is thrown from the top of AB horizontally with a velocity of 10m/s towards CD. Simultaneously another object of mass '2m' is thrown from top of CD at an angle 60degree below horizontal towards AB with the same magnitude of intial velocity as that of the first object. 2 objects move in the same vertical plane, collide in mid air and stick to each other.
i) find 'd'
ii) find position where the objects hit ground
 
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1. Start with these equations:

x=vtcos(\theta)
y=vtsin(\theta)-\frac{1}{2}gt^2

You will need to eliminate t between the two 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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