Question

a rock is thrown with a horizontal velocity in the positive x direction from the top of an 160 m high cliff. the rock strikes the ground 1330 m from the base of the cliff. the drawing is not to scale. how long (time) is the rock in the air prior to hitting the ground (ignoring air resistance)? a 16 s b 9.8 s c 8.31 s d 5.71 s e 33.98 s

Explanation:

Step1: Analyze vertical - motion

The vertical - motion of the rock 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 $y=- 160\ m$ (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 the equation

Since $v_{0y}=0\ m/s$ and $a=-g=-9.8\ m/s^{2}$, the equation simplifies to $y=\frac{-1}{2}gt^{2}$. Rearranging for time $t$, we get $t=\sqrt{\frac{-2y}{g}}$.

Step3: Calculate the time

Substitute $y = - 160\ m$ and $g = 9.8\ m/s^{2}$ into the formula: $t=\sqrt{\frac{-2\times(-160)}{9.8}}=\sqrt{\frac{320}{9.8}}\approx\sqrt{32.65}\approx5.71\ s$.

Answer:

D. 5.71 s