Question

Andy and his friends are playing baseball. They each hit the ball a different distance, shown in the table below. If each child hit the ball from the same place, who most likely hit the ball with the greatest force?
Name Distance
Andy 10 m
Jill 21 m
Susan 16 m
Mike 8 m

Answer 1

Most likely Jill.

Reason: For projectile motion (same launch point, same ball, negligible air resistance) the horizontal range R is R = v^2 sin(2θ)/g. For typical similar launch angles (near the optimum), a larger range means a larger initial speed v (and thus more kinetic energy). If the hitters apply roughly comparable contact times and hit the same ball, a larger change in speed implies a larger force/impulse. Since Jill’s ball went 21 m — the farthest — she most likely applied the greatest force.

Caveat: if launch angles or contact times differ a lot, someone could produce a larger range with a smaller peak force (e.g., by hitting much closer to the optimal 45° angle). But with the usual assumptions, Jill is the best answer.