Question

A rock thrown horizontally at 25 m/s from a cliff that is 45 m high. How far from tag base of the cliff does the rock land?

Answer 1

Answer on Question 49113, Physics, Mechanics | Kinematics | Dynamics

Question:

A rock thrown horizontally at $25\mathrm{m/s}$ from a cliff that is $45\mathrm{m}$ high. How far from tag base of the cliff does the rock land?

Solution:

First we find the time which rock takes to fall from the cliff on the land. Because the initial velocity of the rock along y-axis equals to zero, we can write:

$$h = \frac {1}{2} g t ^ {2},$$

where $h$ is the height of the cliff, $t$ is the time and $g$ is the acceleration of gravity. Therefore, from this formula we obtain the time:

$$t = \sqrt {\frac {2 h}{g}} = \sqrt {\frac {2 \cdot 4 5 m}{9 . 8 m / s ^ {2}}} = 3. 0 3 s.$$

So, we can find how far from tag base of the cliff the rock land:

$$d = v _ {r o c k} t = 2 5 \frac {m}{s} \cdot 3. 0 3 s = 7 5. 7 5 m.$$

Answer:

The rock lands 75.75 meters far from tag base of the cliff.

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