Calculate Energy and Velocity of Thrown Objects: Beach Ball and Fastball

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The discussion focuses on calculating the energy and velocity of two thrown objects: a beach ball and a fastball. For the beach ball, calculations include its maximum height and impact speed, considering both no air resistance and a constant air resistance force of 10N. The fastball's analysis involves determining its gravitational and kinetic energy at release and its speed upon reaching home plate. Participants express confusion over the calculations, particularly regarding the beach ball's maximum height. The thread emphasizes the need to show work for homework assignments to receive assistance effectively.
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1 A beach ball is thrown straight up with a speed of 10m/s from a point 2 m above the ground
a) Assuming no air reistance, calculate how far up the ball will go
b)At what speed will the ball eventually hit the ground?
c) If the air resistance exerts a constant force fo 10N during the journey, calculate the new maximum height and maximum speed of the ball.

2. A pitcher throws a fastball, off target, at a speed of 90 km/h and hits home plate. The ball of mass 0.14 kg is 2.2 m above the ground when it leaves the pither's hand
a)What is the total gravitational and kinetic energy of the ball at the time of release?
b) What is teh ball's kinetic energy when it reaches home plate?
c) How fast is the ball moving when it collides with the home plate?
 
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As this is homework, you'll need to show an attempt first.

What are your thoughts on this?
 
honestly I'm lost
 
for 1 a) i got 50m
by first finding the time
then the distance
t=2/10
=0.2

d=v/t
=10/0.2
 
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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