Calculating Time Interval for Ball to Strike Ground | Ball Velocity Question

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A ball is thrown downward with an initial speed of 7.75 m/s from a height of 30.8 m, and the question is to find the time it takes to hit the ground. The initial attempt to calculate the time using only gravitational acceleration of 9.8 m/s² was incorrect, as it neglected the initial velocity. The ball accelerates at 9.81 m/s², and it's essential to use kinematic equations that account for both initial velocity and acceleration. Participants suggest reviewing constant acceleration equations to solve the problem accurately. Understanding these principles is crucial for correctly determining the time interval for the ball to strike the ground.
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Homework Statement


A ball is thrown directly downward, with an initial speed of 7.75 m/s, from a height of 30.8 m. After what time interval does the ball strike the ground?




The Attempt at a Solution


The way I understand it is that since it is freefalling, it is moving at 9.8m/s towards that ground, thereby I neglected the 7.75m and did 30.8/9.8 = 3.14s..however it is wrong and the similar problem book is even numbered therefore cannot work through it backwards.. Any help?
 
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I am a Newbie said:

The Attempt at a Solution


The way I understand it is that since it is freefalling, it is moving at 9.8m/s towards that ground, thereby I neglected the 7.75m and did 30.8/9.8 = 3.14s..however it is wrong and the similar problem book is even numbered therefore cannot work through it backwards.. Any help?
I'm afraid that is incorrect; the ball is accelerating at 9.81m/s2 which makes a big difference. I'm assuming that your doing a mechanics course, so which kinematic equations do you know?
 
Actually just in a standard Calc based physics, thereby I have no equations
 
Hint: The ball is moving at a constant acceleration.

You should have plenty of constant acceleration equations in a Calculus based Physics course to relate velocity, displacement, acceleration, and time.

If not, check out these...

http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html

CS
 
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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