Answer:
For an object of mass M and velocity V, the kinetic energy is written as:
K = (M/2)*V^2
And also remember that:
1 J = 1 kg*m/s
a) we know that:
Mass = M = 0.7 kg
Velocity = V = 60 m/s
Then the kinetic energy is:
K = (0.7kg/2)*(60m/s)^2 = 1,260 J
b) We know that in a closed system, the energy is conserved.
This means that if we hit an object with an energy E, the maximum energy that we can give to that object is E.
Then if we have a bat of mass M = 2kg, and velocity V = 30m/s
The kinetic energy of the bat (before hitting the ball) is:
K = (2kg/2)*(30m/s)^2 = 900 J
Obviously, this will never happen, because after we hit the ball the bat keeps moving for a bit, meaning that it still has some kinetic energy and it did not transfer all of the kinetic energy to the ball. But we can not have a more precise estimation, because we do not know the mass of the ball and a lot of other needed information, so we can conclude that, the theoretical maximum energy that could be given to the ball, is 900 J.
c) Here we have:
Mass = M = 1950 kg
Velocity = V = 10 m/s
then the energy is:
K = (1950kg/2)*(10 m/s)^2 = 97,500 J.
d) Notice that in the equation of the kinetic energy we have the velocity squared, which means that the contribution of the velocity is larger than the contribution of the mass.
Then the option with the largest velocity most likely would have the largest kinetic energy, then the correct option is the second counting from the top, with a kinetic energy equal to:
K = (0.25 kg/2)*(50m/s)^2 = 312.5 J.
as
. But this cancellation is only valid when 
.
, you end up with the indeterminate form 
, which is why 
is not a zero.