Question

phys 111 - clickers - 2d motion
from the same height and at the same time, one ball is dropped and another is fired horizontally.
which ball has the greater velocity at ground level?
a. the “dropped” ball
b. the “fired” ball
c. they both have the same velocity on impact
d. it depends on how hard the ball was fired
e. it depends on the initial height

Explanation:

Step1: Analyze vertical motion

Both balls start from the same height and have the same initial vertical - velocity ($v_{0y}=0$). Using the kinematic equation $v_y^2 = v_{0y}^2+ 2gh$, where $g$ is the acceleration due to gravity and $h$ is the height. For both balls, $v_{0y} = 0$, so $v_y=\sqrt{2gh}$ at the ground level.

Step2: Analyze horizontal motion

The dropped ball has no initial horizontal velocity ($v_{0x}=0$), so its final velocity $v_d=\sqrt{v_{0x}^2 + v_y^2}=\sqrt{0 + v_y^2}=v_y$. The fired ball has an initial horizontal velocity $v_{0x}
eq0$ and the same vertical - velocity component as the dropped ball at the ground level. Using the Pythagorean theorem for velocity components, $v_f=\sqrt{v_{0x}^2 + v_y^2}$. Since $v_{0x}
eq0$, $v_f>v_d$.

Answer:

B. The “fired” ball