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?

Correct result:

t =  1.4445 s

Solution:

$$\begin{gathered} h=5\text{ m } \\ {v}_0=10\text{ m/s } \\ g=9.81{\text{m/s}}^2 \\ {t}_1=v_0\mathrm{/}g=10\mathrm{/}9.81={\displaystyle \frac{1000}{981}}\doteq 1.0194\text{ s } \\ {h}_1=h+{\displaystyle \frac{1}{2}}\cdot g\cdot t_1^2=5+{\displaystyle \frac{1}{2}}\cdot 9.81\cdot 1.0194^2={\displaystyle \frac{9905}{981}}\doteq 10.0968\text{ m } \\ {h}_1={\displaystyle \frac{1}{2}}\cdot g\cdot t_2^2 \\ {t}_2=\sqrt{2\cdot h_1\mathrm{/}g}=\sqrt{2\cdot 10.0968\mathrm{/}9.81}\doteq 1.4347\text{ s } \\ {t}_3=\sqrt{2\cdot h\mathrm{/}g}=\sqrt{2\cdot 5\mathrm{/}9.81}\doteq 1.0096\text{ s } \\ t+t_3=t_2+t_1 \\ t=t_2+t_1-t_3=1.4347+1.0194-1.0096=1.4445\text{ s} \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Free fall
  How long does the stone fall freely into a depth of 80m? What speed will it hit the bottom of the abyss?
• Rocket start
  The body launched vertically up returns to the start site in 6 seconds. What height did it have?
• Free fall
  The free fall body has gone 10m in the last 0.5s. Find the body speed at the moment of impact.
• 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 it would have to fall on the concrete surface to make the impact intensity the same as in the first case!
• Train 2
  The train slowed down from 90 km/h to 72 km/h in 5 seconds. How long track travel?
• Acceleration
  The car accelerates at rate 0.5m/s². How long travels 400 meters and what will be its speed?
• 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)
• 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.
• 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?
• 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?
• Accelerated motion - mechanics
  The delivery truck with a total weight of 3.6 t accelerates from 76km/h to 130km/h in the 0.286 km long way. How much was the force needed to achieve this acceleration?
• 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)
• Motion
  The two bodies move in the same direction evenly in a straight line, at speeds of 5 cm/s and 10 cm/s. The movement of the first body started 2 seconds earlier than the movement of the second body, from a point located at a distance of 20 cm from the start
• Reconstruction of the corridor
  Calculate how many minutes will be reduced to travel 187 km long railway corridor, where the maximum speed increases from 120 km/h to 160 km/h. Calculate how many minutes will shorten travel time, if we consider that the train must stop at 6 stations, eac
• 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?
• Fall
  The body was thrown vertically upward at speed v₀ = 79 m/s. Body height versus time describe equation ?. What is the maximum height body reach?
• Free fall
  Lloyd fall from height 7 m. Calculate the speed he hit the ground when falling with acceleration g = 9.81 m/s²