Your physical education teacher throws you a tennis ball at a certain velocity, and you catch it. You are now given the following choice: The teacher can throw you a medicine ball (which is much more massive than the tennis ball) with the same velocity, the same momentum, or the same kinetic energy as the tennis ball. 1) Which option would you choose in order to make the easiest catch, and why?2) Explain why you discarded the two other possible choices.3) Provide a numerical example of what would be the final velocity of the medicine ball for the following two cases: same momentum and same kinetic energy.

1) Same momentum

2)See explanation

3)See example in explanation

Explanation:

For first question, we need to understand the relation of momentum and kinetic energy. Formula for momentum is

P = mv

where P is momentum, m is mass and v is velocity

For kinetic energy

KE = 1/2mv2

KE is kinetic energy, m is mass and v is velocity.

Now if you increase velocity or mass, both momentum and kinetic energy will increase.

In the case given in question, the best option is same momentum. Now we will discard the wrong options by elimination method. first we will never choose velocity, because as we know the mass of medicinal ball is much greater than tennis ball. So, if we demand for same velocity, both momentum and kinetic energy will be very high for this increased mass and the effect of collision of medicinal ball with our hands will be devastating. Now, we have to choose between momentum and kinetic energy. Remember, that the mass of medicinal ball is constant, but our choice will effect the velocity. Now, remembering the formulas for both momentum and kinetic energy,

KE = 1/2mv2

P = mv

we can see that for "v" has square on it. So, for a system, kinetic energy will be more in magnitude than the momentum. So, in that relation, you need to have more velocity  if you demand for same kinetic energy for any other system. For example

if m1 = 0.2 kg for tennis ball and v(t) = 5 m/s velocity for tennis ball

P(tennis ball) = 1 kg.m/s

KE(tennis ball) = 2.5 kg.m2/s2

Now look what happens, when you demand for same momentum for medicinal ball of 1 kg.

P(medicinal ball) = 1

so,

1 = 1 x v

v = 1 m/s so velocity reduced from 5 m/s to 1 m/s. . . .(eq1)

Now for same kinetic energy

KE(medicinal ball) = 2.5 kg.m2/s2

2.5 = 1/2 x 1 x v2

v2 = 5

v = 2.2 m/s. . .(eq.2)

Now you can see that for same momentum, you have to bear velocity of 1 m/s but for same kinetic energy you have to bear the velocity of 2.2 m/s. So same momentum is best answer.

Additionally, eq1 and eq 2 are the answers for third question.

do you have a formula possibly

it is a negative acceleration