Question

an object is thrown horizontally from the top of a building. which of the following statements about its motion is correct (ignoring air resistance)? the horizontal velocity increases as the object falls. the vertical motion affects the horizontal motion. the objects speed remains constant throughout its flight. the time it takes to hit the ground depends only on the height of the building.

Explanation:

Step1: Analyze horizontal motion

In the horizontal - direction (ignoring air resistance), there is no acceleration ($a_x = 0$). According to the kinematic equation $v_x=v_{0x}+a_xt$, with $a_x = 0$, the horizontal velocity $v_x$ remains constant as the object falls. So the statement "The horizontal velocity increases as the object falls" is incorrect.

Step2: Analyze independence of motions

The horizontal and vertical motions of a projectile are independent of each other. The vertical motion is a free - fall motion with an acceleration $a_y = g$ (downward), and the horizontal motion is a uniform motion. So the statement "The vertical motion affects the horizontal motion" is incorrect.

Step3: Analyze the speed

The speed of the object is $v=\sqrt{v_x^{2}+v_y^{2}}$. The vertical velocity $v_y$ changes due to the acceleration of gravity ($v_y = v_{0y}+gt$, and $v_{0y}=0$ for a horizontally - thrown object), while $v_x$ is constant. So the speed $v$ changes during the flight, and the statement "The object's speed remains constant throughout its flight" is incorrect.

Step4: Analyze the time of flight

For the vertical motion, the displacement $y=-h$ (taking downwards as negative and the starting - point as the origin), and the kinematic equation $y = v_{0y}t+\frac{1}{2}a_yt^{2}$. Since $v_{0y} = 0$ and $a_y=-g$, we have $-h=0\times t-\frac{1}{2}gt^{2}$, and $t=\sqrt{\frac{2h}{g}}$. So the time it takes to hit the ground depends only on the height of the building.

Answer:

The time it takes to hit the ground depends only on the height of the building.