Determining Force & Direction of 6 kg Particle's Motion

AI Thread Summary
To determine the force and direction of a 6 kg particle's motion, the velocity is expressed as v = (5ti + 4t^2j) m/s. The net force on the particle is given as 43 N, which can be analyzed using the equation F = ma. To find the acceleration vector, one should derive it from the velocity vector. This involves calculating the derivative of the velocity with respect to time, leading to the acceleration components. The discussion emphasizes understanding the relationship between force, mass, and acceleration to solve the problem effectively.
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Homework Statement



The velocity of a 6 kg particle is given by v = (5ti + 4t2j ) m/s, with time t in seconds. At the instant the net force on the particle has a magnitude of 43 N, what are the direction (relative to the positive direction of the x axis) of (a) the net force and (b) the particle's direction of travel?

Homework Equations



F= ma



The Attempt at a Solution



I don't know what to do can someone give me a hint?
 
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If you're familiar with momentum, you'll notice that the rate of change of momentum is force (or you could simply note that the rate of change of velocity is acceleration). Just derive the acceleration vector from the velocity vector.
 
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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