Question

(02.05 mc)
the taipei world financial center is 509 meters high. a dense rock is dropped from the top of the building. neglecting air resistance, how long does it take for the rock to reach the ground?

a 7.21 s
b 10.2 s
c 14.4 s
d 104 s

question 9 (4 points)
(02.05 lc)
the gravitational force between two objects
a increases as the volumes of the objects increase
b increases as the distance between objects decreases
c decreases as the masses of the objects increase
d decreases as the air between object decreases

Explanation:

Step1: Identify the kinematic - equation

The kinematic equation for free - fall motion is $h = v_0t+\frac{1}{2}gt^2$. Since the rock is dropped, $v_0 = 0$. So the equation simplifies to $h=\frac{1}{2}gt^2$, where $h$ is the height, $g$ is the acceleration due to gravity ($g = 9.8\ m/s^2$), and $t$ is the time.

Step2: Solve for time $t$

From $h=\frac{1}{2}gt^2$, we can re - arrange it to get $t=\sqrt{\frac{2h}{g}}$. Given $h = 509\ m$ and $g = 9.8\ m/s^2$, then $t=\sqrt{\frac{2\times509}{9.8}}=\sqrt{\frac{1018}{9.8}}\approx\sqrt{103.88}\approx10.2\ s$.

For the second question:
The gravitational force between two objects is given by $F = G\frac{m_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them.

• The gravitational force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between them.
• As the distance $r$ between the objects decreases, the gravitational force $F$ increases.

Answer:

For the first question: b. 10.2 s
For the second question: b. Increases as the distance between objects decreases