Question

A hobbit throws a ring into a volcano with a horizontal velocity of 20 m/s. If the ring lands

in the lava 3.5 seconds later, how much vertical distance is there between the hobbit and
the lava?

Answer 1

The vertical distance between the hobbit and the lava when the ring lands is calculated using the equation of motion for uniformly accelerated motion. With an initial vertical velocity of 0, an acceleration due to gravity of 9.81 m/s², and a time of 3.5 seconds, the vertical distance is approximately 60.11 meters.

Step-by-step explanation:

The question involves calculating the vertical distance a ring travels after being thrown with horizontal velocity into a volcano, which is a projectile motion problem in physics.

To find the vertical distance, we can use the formula for the displacement in the vertical direction under the influence of gravity, which is s = ut + (1/2)at2, where u is the initial vertical velocity (which is 0 in this case, since the ring is thrown horizontally), a is the acceleration due to gravity (9.81 m/s2), and t is the time the ring is in the air (3.5 seconds). The calculation is as follows:

s = (1/2) * 9.81 m/s2 * (3.5 s)2

s = 4.905 m/s2 * 12.25 s2

s = 60.11 m

Therefore, the vertical distance between the hobbit and the lava when the ring lands is approximately 60.11 meters.