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 fast (velocity) is the rock traveling horizontally prior to hitting the ground (ignoring air resistance)? a 16 m/s b 5.71 m/s c 339.8 m/s d 8.31 m/s e 232.9 m/s

Explanation:

Step1: Calculate time of fall

Use vertical - motion equation $h = v_{0y}t+\frac{1}{2}gt^{2}$. Since the rock is thrown horizontally, $v_{0y} = 0$. So $h=\frac{1}{2}gt^{2}$, and $t=\sqrt{\frac{2h}{g}}$. Given $h = 160$ m and $g = 9.8$ m/s², $t=\sqrt{\frac{2\times160}{9.8}}\approx\sqrt{\frac{320}{9.8}}\approx5.71$ s.

Step2: Calculate horizontal velocity

In horizontal direction (no acceleration, $a_x = 0$), $v_x=\frac{x}{t}$. Given $x = 1330$ m and $t\approx5.71$ s, $v_x=\frac{1330}{5.71}\approx232.9$ m/s.

Answer:

E. 232.9 m/s