How to Find the Maximum Range of a Ball Shot from a Spring Gun?

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To find the maximum range of a ball shot from a spring gun, start by calculating the velocity using the equation 1/2 kx^2 = 1/2 mv^2, where k is the spring constant and x is the compression distance. After determining the velocity, apply projectile motion equations to find the time of flight. The horizontal range can then be calculated using the formula distance = velocity x time of flight. It's important to note that gravitational force (F = mg) does not directly apply to finding the range in this context. This method provides a systematic approach to solving the problem effectively.
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Homework Statement


a 15 g ball is shot from a spring gun whose spring has a force constant600 N/m the spring is compressed by 5cm the greatest posible horizontal range of the ball for this compression is


Homework Equations





The Attempt at a Solution


what equation should i use to find the distance i know the enrgy stored

i used i/2 k x2 = F.s

then put F = mg the answer doesn't come
 
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Hello Vipul. you are mistaken. F = mg is gravitational force, which is not the acting force for the required answer.

use 1/2 kx^2 = 1/2mv^2 and find velocity. then use equations of projectile motion, find time of flight(t), and v.t = distance.
 
Hello Vipul. you are mistaken. F = mg is gravitational force, which is not the acting force for the required answer.

use 1/2 kx^2 = 1/2mv^2 and find velocity. then use equations of projectile motion, find time of flight(t), and v.t = distance.
 
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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