How to Find initial Velocity at 90 degrees with only a time variable given

AI Thread Summary
To find the initial velocity of a nerf dart launched at 90 degrees, the key information includes the launch height of 1.953 feet and the total flight time of 0.43 seconds. The discussion emphasizes the need to apply relevant physics equations, particularly those related to projectile motion and kinematics. Participants are reminded to provide an attempted solution as per forum guidelines, which encourages engagement and deeper understanding. The conversation highlights the importance of identifying the correct concepts and equations to solve the problem effectively. Understanding these principles is crucial for calculating the initial velocity accurately.
cloakblade5
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I am given the information that a nerf dart is launched upwards at a 90 degrees with the top of the launcher at 1.953ft and that it hits the ground .43 seconds later. I am then tasked with finding the initial velocity of the launcher and I have no idea where to start.
 
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cloakblade5 said:
I am given the information that a nerf dart is launched upwards at a 90 degrees with the top of the launcher at 1.953ft and that it hits the ground .43 seconds later. I am then tasked with finding the initial velocity of the launcher and I have no idea where to start.
Welcome to PF cloakblade5,

You must have some idea as where to start, which concept(s) are involved? What are the relevant equations?

Please be aware the according to our forum guidelines, you are required to post an attempted solution when asking for homework assistance.
 
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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