a rock is blown out of a volcano when it started to fall from its highest point at 9.5 seconds to hit the ground
1 answer:
Answer:
<em>The rock reaches a maximum height of 442.225 m and was thrown at a speed of 93.1 m/s</em>
Explanation:
<u>Vertical Launch</u>
The rock is launched up with a certain speed vo, it reaches its highest point at a height h when the speed is zero, and then it stars a free-fall motion until it hits the ground at time t.
The maximum height is given by
The rock takes the same time to reach this point as to return to the ground, thus we can calculate the maximum height
The rock was thrown up at a speed
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Answer:
x = 0.40 m
Explanation:
- When the displacement is maximum, the particle is momentarily at rest, which means that at this point (assuming no friction present) all the mechanical energy is elastic potential, which can be written as follows:
- Since in absence of friction, total mechanical energy must keep constant, this means that at any time, the sum of the kinetic and potential energy, must be equal to (1), as follows:
- If KEf = U/2f, replacing in (2), we get:
- At any point, the elastic potential energy is given by the following expression:
where k= spring constant (N/m) and x is the displacement from the
equilibrium position.
- Replacing (4) in (3), simplifying and rearranging, we get:
- Finally, solving for x, we get: