examkrackers physics 1001 # 324

[2010premed]

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A 2kg ball and a 4kg ball are thrown upwards each with a speed of 20m/s. At what height will the 2 kg ball be, when the kinetic energy of the balls are equal?
Answer: 20m

The answer says: ideal projectile motion is independent of mass, so both will have the same velocity at all times. Thus, only when their velocities are zero, will their kinetic energies be zero.

Can some1 please explain?

 

[lorenzomicron]

ok, so irregardly of mass, the acceleration each ball will experience is 9.8m/s^2, which is just basic gravity.

if they are thrown up at the same speed initially, and acceleration is the same, then they will always have the same velocity:
v= 20-a*t, independent of mass because acceleration in this context is independent of mass

the kinetic energy is k=1/2mv^2, if the velocity v is always the same, then the kinetic energy of the 4 kg ball is always more than that of the 2 kg ball because 4 kg is a bigger mass m than 2 kg.

thus, the only way the kinetic energy will be equal is if v=0, at that instant, k=0

make sense?

 

[2010premed]

Ohhhhhhhhhhhhhhhhhhhhhhhhhhh..... and the velocity is 0 at maximum height... ok now it makes sense.
Thanks a lot!!