Question

question 8 of 10
a ball rolls horizontally off a table of height 0.6 m with a speed of 9 m/s. how long does it take the ball to reach the ground?
a. 1.2 s
b. 15 s
c. 0.35 s
d. 0.067 s

Explanation:

Step1: Identify vertical - motion equation

The ball's vertical - motion is a free - fall motion. The vertical displacement $y - y_0=-h$ (taking downwards as negative), the initial vertical velocity $v_{0y} = 0\ m/s$, and the acceleration $a=-g=- 9.8\ m/s^{2}$. The equation for vertical displacement is $y - y_0=v_{0y}t+\frac{1}{2}at^{2}$.

Step2: Substitute values into the equation

Substituting $y - y_0=-0.6\ m$, $v_{0y} = 0\ m/s$, and $a=-9.8\ m/s^{2}$ into $y - y_0=v_{0y}t+\frac{1}{2}at^{2}$, we get $-0.6=0\times t+\frac{1}{2}\times(-9.8)t^{2}$.

Step3: Solve for $t$

The equation simplifies to $4.9t^{2}=0.6$. Then $t^{2}=\frac{0.6}{4.9}$, and $t=\sqrt{\frac{0.6}{4.9}}\approx0.35\ s$.

Answer:

C. 0.35 s