a coin is dropped from the top of a building and travels in free fall. after 3.50 s, the coin hits the…

Explanation:

Step1: Identify the kinematic - equation

The kinematic equation for vertical displacement in free - fall with initial velocity $v_0 = 0$ is $\Delta y=v_0t+\frac{1}{2}at^{2}$. Since the coin is dropped, $v_0 = 0$. The equation simplifies to $\Delta y=\frac{1}{2}at^{2}$.

Step2: Substitute the values

We know that $a=- 9.8\ m/s^{2}$ and $t = 3.50\ s$. Substitute these values into the equation: $\Delta y=\frac{1}{2}\times(-9.8\ m/s^{2})\times(3.50\ s)^{2}$. First, calculate $(3.50\ s)^{2}=3.50\times3.50 = 12.25\ s^{2}$. Then, $\frac{1}{2}\times(-9.8\ m/s^{2})\times12.25\ s^{2}=-4.9\ m/s^{2}\times12.25\ s^{2}=-60.025\ m$. The negative sign indicates the direction is downward.

Answer:

$60.0$ (rounded to one decimal place)