What is the impact velocity of a rock thrown horizontaly from a cilff?

Answer 1

The impact velocity of a rock thrown horizontal from a cliff depends on two things, the initial speed of the rock (vi) and the height of the cliff (h). The final velocity (impact velocity) is represented by vf

For this formula, air resistance is neglected, and acceleration due to gravity is assumed to be 9.8 m/s2. The acceleration is positive here because down is being treated as the positive direction. You will get the same result if you use negative 9.8 m/s2 and make the height negative. sqr() means square root.

vf = sqr(19.6h + vi2)

For example if the rock was thrown off a 3 meter high cliff at 20 m/s, the impact velocity would be sqr(19.6 x 3 + 202), which would be sqr(58.8 + 202), which would be 21.42 m/s.

The angle relative to the ground is the inverse tangent of sqr(19.6h)/vi

which in this case is tan-1( sqr(19.6 x 3)/20), which is tan-1(7.67/20) which is 21.0 degrees.