Question

Astronaut Mary is standing at the edge of a vertical cliff a distance h above horizontal ground on a distant planet. She performs an experiment where she throws a magnetized steel ball horizontally off the cliff with initial speed v. After leaving Mary’s hand, the ball undergoes a horizontal displacement D before landing on the ground. Only gravity acts on the ball during this flight. Mary repeats this experiment. However, during this 2nd experiment, a strong magnet is placed nearby which provides the otherwise free-falling ball with a constant component of horizontal acceleration (Q) toward the cliff in addition to the constant downward component of acceleration (g). As a result, the ball reaches the ground after undergoing a horizontal displacement L which is less than D of the first experiment.

In terms of quantities that do not extend beyond the list (h, v, Q and D), determine expressions for the following quantities:
a) the time interval between the moment the ball leaves Mary’s hand to the moment before the ball reaches the ground for the first experiment;

b) the vertical component of freefall acceleration g of this planet; and c) The horizontal distance L of the 2nd experiment.

d) Assuming the ball lands directly below Mary (i.e. at the base of the cliff) at the moment it reaches the ground in the 2nd experiment, Determine an expression for Q of the 2nd experiment in terms of quantities that do not extend beyond the list (h, v, and D).

Answer 1