We can solve this problem using the conservation of energy principle:
Initial potential energy = Final kinetic energy
The initial potential energy is equal to the potential energy at the top of the tower:
PE = mgh
where m is the mass of the ball, g is the acceleration due to gravity (9.81 m/s^2), and h is the height of the tower (46.6 m).
PE = (0.1557 kg)(9.81 m/s^2)(46.6 m) = 71.9 J
The final kinetic energy of the ball just before impact can be calculated using the formula:
KE = 1/2 mv^2
where m is the mass of the ball and v is its velocity.
Since the ball was dropped from rest, its initial velocity was zero. Therefore, all of the potential energy at the top of the tower is converted to kinetic energy just before impact.
PE = KE
71.9 J = 1/2 (0.1557 kg) v^2
v^2 = (2 × 71.9 J) / 0.1557 kg = 828.6
v = sqrt(828.6) = 28.8 m/s (rounded to one decimal place)
The velocity of the ball just before impact is 28.8 m/s.
The kinetic energy of the ball just before impact can be calculated using the formula:
KE = 1/2 mv^2
where m is the mass of the ball and v is its velocity.
KE = 1/2 (0.1557 kg) (28.8 m/s)^2 = 61.7 J (rounded to one decimal place)
Therefore, the ball has 61.7 J of kinetic energy just before impact.