Question

question 20 (problem reference 3 - 3) a shell is fired with a horizontal velocity in the positive x - direction from the top of an 80 - m high cliff. the shell strikes the ground 1330 m from the base of the cliff. the drawing is not to scale. how long is the shell in the air? a. 8.2 s b. 12 s c. 4.0 s d. 16 s

Explanation:

Step1: Analyze vertical - motion

The shell's vertical - motion is a free - fall motion. The initial vertical velocity $v_{0y}=0\ m/s$, the acceleration due to gravity $g = 9.8\ m/s^{2}$, and the vertical displacement $y=- 80\ m$ (taking downwards as negative). The equation for vertical displacement in free - fall is $y = v_{0y}t+\frac{1}{2}at^{2}$.

Step2: Substitute values into equation

Since $v_{0y} = 0\ m/s$, the equation simplifies to $y=\frac{1}{2}at^{2}$, where $a=-g=-9.8\ m/s^{2}$. So, $-80=\frac{1}{2}\times(-9.8)t^{2}$.

Step3: Solve for time $t$

First, rewrite the equation as $t^{2}=\frac{2\times80}{9.8}$. Then $t=\sqrt{\frac{160}{9.8}}\approx4.0\ s$.

Answer:

C. 4.0 s