Question

question 8 of 25
a pencil is rolled off a table of height 0.92 m. if it has a horizontal speed of 1.4 m/s, how long does it take the pencil to reach the ground?
a. 0.85 s
b. 0.66 s
c. 0.43 s
d. 1.52 s

Explanation:

Step1: Identify vertical - motion equation

The vertical - displacement of the pencil is given by the equation $y = y_0+v_{0y}t+\frac{1}{2}a_y t^2$. The initial vertical position $y_0 = 0.92$ m, the initial vertical velocity $v_{0y}=0$ m/s, and the acceleration due to gravity $a_y=- 9.8$ m/s² (taking downwards as negative), and the final vertical position $y = 0$ m.
So the equation becomes $0 = 0.92+0\times t-\frac{1}{2}\times9.8t^2$.

Step2: Solve for time $t$

We have the equation $4.9t^2=0.92$. Then $t^2=\frac{0.92}{4.9}$, and $t=\sqrt{\frac{0.92}{4.9}}\approx0.43$ s.

Answer:

C. 0.43 s