What is the initial velocity of a rock thrown off a 20-m high cliff?

  • Thread starter hansel13
  • Start date
In summary, the problem involves a rock being thrown horizontally from a cliff and striking the ground at a 45 degree angle. The equations provided involve the range and velocity of the rock. By considering the x and y components of the final velocity and using the equation for final y velocity with the initial y velocity being 0, the correct answer of 20m/s can be found.
  • #1
hansel13
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Homework Statement


A rock is thrown horizontally from the top of a 20-m high cliff and strikes the ground at an angle of 45 degrees. With what speed was it thrown?


Homework Equations


R = V2/g*sin(2theta)
v2 = (v0*sin(theta))2 - 2gy

The Attempt at a Solution



I have 2 unknowns no matter what equation I try to use. I've tried to get it down to one unknown, but I keep getting the wrong answer..
 
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  • #2
Don't think in equations, think in terms of the picture you see. You grabbed the range equation, but don't just try to plug things into it.

The rock strikes the ground at 45 degrees. That means it's final velocity has x and y components that are related to each other how? You know x velocity is constant. You can find final y velocity using that initial y velocity is zero. If you know the relation between x and y velocity, you can then find x velocity.
 
  • #3
Ahhh, I think I understand now.

v2 = 0 - 2gy
v = (2*9.8*20)1/2
= 19.7

The correct answer is 20m/s. Thanks :smile:
 

1. What factors affect the distance a stone travels when thrown off a cliff?

The distance a stone travels when thrown off a cliff is primarily influenced by the initial velocity and angle of the throw, as well as the air resistance and gravity acting on the stone. Other factors such as wind speed and direction may also play a role.

2. How does the mass of the stone impact its trajectory when thrown off a cliff?

The mass of the stone does not significantly affect its trajectory when thrown off a cliff, as long as the initial velocity and angle of the throw remain constant. This is because the force of gravity acting on the stone is directly proportional to its mass, resulting in the same acceleration for all objects regardless of their mass.

3. Why does a stone thrown off a cliff follow a curved path?

A stone thrown off a cliff follows a curved path due to the combined effects of its horizontal velocity and the force of gravity acting on it. As the stone moves forward, gravity pulls it downward, resulting in a parabolic trajectory.

4. Can the height of the cliff affect the distance a stone travels when thrown off it?

Yes, the height of the cliff can impact the distance a stone travels when thrown off it. The higher the cliff, the longer the stone has to travel before hitting the ground, resulting in a longer horizontal distance. However, if the initial velocity and angle of the throw remain constant, the difference in distance may not be significant.

5. How does air resistance affect the motion of a stone thrown off a cliff?

Air resistance, also known as drag, can slow down the horizontal velocity of a stone thrown off a cliff. This can result in a shorter distance traveled and a lower final velocity upon impact. However, the effect of air resistance is minimal for most objects thrown off a cliff due to the relatively short distance and high initial velocity involved.

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