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?

Correct answer:

E =  882.9 kJ

Step-by-step explanation:

$$\begin{gathered} m=720\text{ kg } \\ h=125\text{ m } \\ g=9.81{\text{m/s}}^2 \\ h={\displaystyle \frac{1}{2}}g{t}^2 \\ t=\sqrt{2\cdot h\mathrm{/}g}=\sqrt{2\cdot 125\mathrm{/}9.81}\doteq 5.0482\text{ s } \\ v=g\cdot t=9.81\cdot 5.0482\doteq 49.5227\text{ m/s } \\ {E}_1={\displaystyle \frac{1}{2}}\cdot m\cdot v^2={\displaystyle \frac{1}{2}}\cdot 720\cdot 49.5227^2\doteq 882900\text{ J } \\ E=E_1\to \text{ kJ}=E_1\mathrm{/}1000\text{ kJ}=882900\mathrm{/}1000\text{ kJ}=882.9\text{ kJ}={\displaystyle \frac{8829}{10}}\text{ kJ}=882.9\text{ kJ} \end{gathered}$$

Try another example

Related math problems and questions:

• The elevator
  The elevator car weighing 400 kg rises from the third to the fifth floor. By what value will the potential gravitational energy of the cabin increase? What useful work will the elevator motor do? The height of one floor is 5m .
• 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?
• Positional energy
  What velocity in km/h must a body weighing 60 kg have for its kinetic energy to be the same as its positional energy at the height 50 m?
• Elevator
  In homes with more floor elevators are used. For passenger transport, the most commonly used traction elevator counterweight. The top of the shaft engine room with the engine. The car is suspended on a rope, which is guided up over two pulleys to the coun
• Car
  At what horizontal distance reaches the car weight m = 753 kg speed v = 74 km/h when the car engine develops a tensile force F = 3061 N. (Neglect resistance of the environment.)
• Power input
  The construction lift lifted a load weighing 300 kg to a height of 12 m with a uniform movement. How long has it taken for the load to be lifted if the efficiency is 75% and the engine has a power input of 5 kW?
• 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
• Electric cooker
  During which time t does an electric cooker with power input P = 500 W and with efficiency n = 75% heat water with mass m = 2 kg and temperature t1 = 10°C to the boiling point (t2 = 100°C). The specific heat capacity of water is c = 4 180 J. Kg-1. K-1
• Free fall
  Lloyd fall from height 7 m. Calculate the speed he hit the ground when falling with acceleration g = 9.81 m/s²
• Free fall
  The free fall body has gone 10m in the last 0.5s. Find the body speed at the moment of impact.
• A hammer
  A hammer weighing 500 g hits the nail at a speed of 3 m/s. What is the average force acting on the nail, which penetrates the board to a depth of 5 cm?
• 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!
• Driver
  The car driver drives at a speed of 100 km/h, saw the obstacle, and began to brake with a slowing of 5 m/s². What is the length of the pathway to stopping the car when the driver has registered the obstacle with a delay of 0.7 s?
• Acceleration
  The car accelerates at rate 0.5m/s². How long travels 400 meters and what will be its speed?
• Ice floe
  What is the volume of an ice floe weighing 326 kg? The density of ice is only 920 kg/m³.
• Sweets
  We want to prepare 5 kg of sweets for 150 CZK. We will mix cheaper candy: 1 kg for 120 CZK and more expensive candy: 1 kg per 240 CZK. How much of these two types of candy is necessary to prepare this mixture?
• Mixture of coffee
  They have to prepare a mixture of coffee in packing centres so that 1 kg costs 240 CZK. There are two types of coffee in stock at the price of 220 CZK per 1 kg and 300 CZK per 1 kg. How many kilograms of each species need to be mixed to prepare 50 kg of t