Happy Holidays!
Recall the equation for kinetic energy:
[tex]\large\boxed{KE = \frac{1}{2}mv^2 (J)}}[/tex]
m = mass (Kg)
v = velocity (m/s)
KE = kinetic energy (Nm or J)
We can find the kinetic energy for both the bowling ball and baseball:
Bowling ball:
[tex]\large\boxed{KE = \frac{1}{2}(4)(10^2) = 200 J}[/tex]
Baseball:
[tex]\large\boxed{KE = \frac{1}{2}(.25)(50^2) = 312.5 J}[/tex]
Since 312.5 J > 200 J, the BASEBALL has the greater kinetic energy. Thus, it would exert a greater impact force than the bowling ball, so it would hurt more.