Does velocity affect the kinetic energy of falling objects?

AI Thread Summary
The discussion centers on the kinetic energy of three identical balls thrown from a cliff with the same initial speed but in different directions. Despite initial assumptions, all three balls have equal kinetic energy just before hitting the ground. This is because, after reaching their peak, the first ball's downward velocity matches its initial upward velocity, leading to the same final speed as the other two balls. The key takeaway is that the time spent in the air does not affect the kinetic energy at impact, as all balls convert potential energy to kinetic energy equally. The conclusion is that kinetic energy is determined solely by the speed at which the balls hit the ground, not their initial trajectories.
mohabitar
Messages
140
Reaction score
0
Three identical balls are thrown from the edge of a cliff, each with the same initial speed. Ball 1 is thrown directly upward. Ball 2 is thrown directly downward. Ball 3 is thrown horizontally. Which of the following statements correctly characterizes the relative kinetic energies (K) of the three balls just before hitting the ground.

The correct answer for this is that theyre all equal, but that doesn't make sense to me. If the first ball is thrown directly upward, then when its done climbing the top, it will have more time to accelerate downward than all the other balls. The more time it has to accelerate, the faster it's velocity will become, and KE=1/2MV^2, so the larger the velocity, the larger the KE. And ball 2 and 3 having the same KE makes sense, but I figured ball 1 should be greater. Where did I go wrong?
 
Physics news on Phys.org
Determine the velocity when the first ball, falling down from the top height, reaches the edge of the cliff again. You will see that it is equal in magnitude as the initial velocity was. From here, it moves as ball 2. ehild
 
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}...
View full post »

Similar threads

Potential and Kinetic energy equations including drag coefficient
Replies
1
Views
1K
Question about the Kinetic Energy of a baseball in flight
Replies
8
Views
3K
Kinetic Energy & Momentum of a Ball released from Spring
Replies
6
Views
2K
Catapult spring, Kinetic and Potential energy
Replies
10
Views
3K
Kinetic Energy of a Cylinder Rolling Without Slipping
Replies
21
Views
4K
Projectile Motion : Work and Energy
Replies
4
Views
1K
Internal energy of a gas and kinetic energy, "typical velocity"
Replies
5
Views
803
Resistance force changing the velocity of an object
Replies
8
Views
1K
A ball climbing a ramp while "rolling the wrong way"
Replies
32
Views
3K
Calculating Kinetic Energy of a Ball: Is it Possible?
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top