Free fall

How long does the stone fall freely into a depth of 80m? What speed will it hit the bottom of the abyss?

Correct answer:

t =  4.0386 s
v =  39.6182 m/s

Step-by-step explanation:

$$\begin{gathered} s={\displaystyle \frac{1}{2}}g{t}^2 \\ g=9.81{\text{m/s}}^2 \\ s=80\text{ m } \\ t=\sqrt{{\displaystyle \frac{2\cdot s}{g}}}=\sqrt{{\displaystyle \frac{2\cdot 80}{9.81}}}=4.0386\text{ s} \end{gathered}$$

$v=g\cdot t=9.81\cdot 4.0386=39.6182\text{ m/s}$

Try another example

Related math problems and questions:

• Abyss
  The stone fell into the abyss: 2 seconds after we heard hitting bottom. How deep is the abyss (neglecting air resistance)? (gravitational acceleration g = 9.81 m/s² and the speed of sound in air v = 343 m/s)
• Free fall
  For how long and at what speed does the body fall to the ground during a free fall from a height of 35 m?
• Up and down motion
  We throw the body from a height h = 5 m above the Earth vertically upwards v0 = 10 m/s. How long before we have to let the second body fall freely from the same height to hit the Earth at the same time?
• Free fall
  The free fall body has gone 10m in the last 0.5s. Find the body speed at the moment of impact.
• Free fall
  Lloyd fall from height 7 m. Calculate the speed he hit the ground when falling with acceleration g = 9.81 m/s²
• Acceleration
  The car accelerates at a rate of 0.5 m/s². How long travels 400 meters, and what will be its speed?
• Free fall
  The elevator car weighing 720 kg is torn off at a height of 125 m and begins to fall in a free fall. How much kinetic energy does the elevator car have when it hits the ground floor of the building, when the free fall of the car lasted 5 s?
• Gravitation
  From the top of the 80m high tower, the body is thrown horizontally with an initial speed of 15 m/s. At what time and at what distance from the foot of the tower does the body hit the horizontal surface of the Earth? (use g = 10 ms-2)
• Acceleration 2
  if a car traveling at a velocity of 80 m/s/south accelerated to a velocity of 100 m/s east in 5 seconds, what is the cars acceleration? using Pythagorean theorem
• Brakes
  The braking efficiency of a passenger car is required to stop at 12.5 m at an initial speed of 40 km/h. What is the acceleration braking by brakes?
• Free fall 5
  Jeremy accidently dropped his toy stuffed animal from the balcony of his apartment on the fourth floor. The toy hit the ground at a velocity of 16.0 meters/second. At impact, it took 2.0 seconds for the toy’s velocity to reach 0 meters/second. If the toy
• The projectile
  The projectile was fired horizontally from a height of h = 25 meters above the ground at a speed of v0 = 250 m/s. Find the range and flight time of the projectile.
• The car
  The car weight 1280 kg, increased its speed from 7.3 m/s to 63 km/h on a track of 37.2 m. What force did the car engine have to exert?
• Bomber
  The aircraft flies at an altitude of 4100 m above the ground at speed 777 km/h. At what horizontal distance from the point B should be release any body from the aircraft body to fall into point B? (g = 9.81 m/s²)
• The projectile
  The projectile leaves the 10 m long barrel at an instantaneous speed of 500 m/s. What is the acceleration of the movement of the projectile in the barrel and in what time will the projectile pass the barrel if, we assume that the movement was evenly accel
• A car
  A car weighing 1.05 tonnes driving at the maximum allowed speed in the village (50 km/h) hit a solid concrete bulkhead. Calculate height would have to fall on the concrete surface to make the impact intensity the same as in the first case!
• Collision
  The two bodies, whose initial distance is 240 m, move evenly against each other consistently. The first body has an initial velocity of 4 m/s and an acceleration of 3 m/s², the second body has an initial speed of 6 m/s and an acceleration of 2 m/s². Fin