Question

A batter checks her swing as a 0.15-kg baseball crosses home plate outside the strike zone. If the separation between the batter and the ball is 0.77 m and the gravitational force exerted on the batter by the ball is 1.1 x 10^-9 N, what is the mass of the batter?

Answer 1

The mass of the batter is approximately 0.971 kg.

Step-by-step explanation:

The gravitational force exerted on the batter by the baseball can be used to calculate the mass of the batter. We can use Newton's law of gravitation:

F = G * (m1 * m2) / r^2

Where F is the gravitational force, G is the gravitational constant (approximately 6.6743 × 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the separation between the objects.

In this case, the gravitational force is given as 1.1 x 10^-9 N, the mass of the baseball is 0.15 kg, and the separation between the batter and the ball is 0.77 m. Plugging in these values into the equation and solving for the mass of the batter (m2), we get:

m2 = (F * r^2) / (G * m1) = (1.1 x 10^-9 N * (0.77 m)^2) / (6.6743 × 10^-11 N m^2/kg^2 * 0.15 kg) = 0.971 kg