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?

Correct answer:

v =  112.7553 km/h

Step-by-step explanation:

$$\begin{gathered} m=60\text{ kg } \\ h=50\text{ m } \\ g=9.81{\text{m/s}}^2 \\ E=m\cdot g\cdot h=60\cdot 9.81\cdot 50=29430\text{ J } \\ E={\displaystyle \frac{1}{2}}m{v}^2 \\ {v}_1=\sqrt{{\displaystyle \frac{2\cdot E}{m}}}=\sqrt{{\displaystyle \frac{2\cdot 29430}{60}}}=3\sqrt{109}\text{ m/s}\doteq 31.3209\text{ m/s } \\ v=v_1\to \text{ km/h}=v_1\cdot 3.6\text{ km/h}=31.3209\cdot 3.6\text{ km/h}=112.755\text{ km/h}=112.7553\text{ km/h} \end{gathered}$$

Try another example

Related math problems and questions:

• Swing
  A child weighing 12 kg is sitting on a swing at a distance of 130 cm from the rotation axis. How far away from the rotation (center) axis must sit down his mother weighs 57 kg if she wants to be a swing in balance?
• 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?
• 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 .
• A stone
  There is a stone weighing 60 kg on the billet. The distance from the support point to the stone is 20cm. The length of the billet is 1m. Determine the force exerted by the hand at the end of the billet.
• 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?
• 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!
• Vacation
  Parents piggybacking children on vacation to its grandmother and grandfather at a city distant 150 kilometers. They agreed to meet halfway. Parents will be travel at 90 km/h, grandmother and grandfather at 60 km/h. Parents depart at 12:00 hours. When gran
• Chained winch
  When digging a well, a chained winch is used to balance the material. An empty shackle weighs 8 kg, a full 64 kg. What force must the worker exert on the crank handle when pulling the shackle with a uniform movement from a depth of 5 m if the shaft diamet
• 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.)
• The bridge
  A vehicle weighing 5,800 kg passes 41 km/h on an arched bridge with a radius of curvature of 62 m. What force is pushing the car onto the bridge as it passes through the center? What is the maximum speed it can cross over the center of the bridge so that
• Cars motion
  From point A car start at the speed of 90 km/h. Against it departs from the point B at the same time another car at 60 km/h. For how long and where they met if the distance between A and B is 180 km?
• 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?
• Hollow sphere
  The steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and the density of steel is 7850 kg/m³
• Floating of wood - Archimedes law
  What will be the volume of the floating part of a wooden (balsa) block with a density of 200 kg/m³ and a volume of 0.02 m³ that floats in alcohol? (alcohol density is 789 kg/m³)
• Two cities
  The car goes from city A to city B at an average speed of 70 km/h, back at an average speed of 50 km/h. If it goes to B and back at an average speed of 60 km/h, the whole ride would take 8 minutes less. What is the distance between cities A and B?
• Foot area
  Which animal will leave deeper footstep: an elephant weighing 5 tons with a total foot area of 0.5 square meters, or a gazelle weighing 10 kg and a foot area of 50 cm square?
• Two cars
  Two cars started against each other at the same time to journey long 346 km. The first car went 53 km/h and the second 53 km/h. What distance will be between these cars 20 minutes before meet?