# Free fall

The free fall body has gone 10m in the last 0.5s. Find the body speed at the moment of impact.

Result

v =  22.5 m/s

#### Solution:

$t=0.5 \ \text{s} \ \\ s=10 \ \text{m} \ \\ \ \\ g=10 \ \text{m/s}^2 \ \\ \ \\ \ \\ \ \\ s=\dfrac{ 1 }{ 2 } \cdot \ g \cdot \ t_{1}^2 - \dfrac{ 1 }{ 2 } \cdot \ g \cdot \ (t_{1}-t)^2 \ \\ 2 \cdot \ s/g=t_{1}^2 - (t_{1}-t)^2 \ \\ 2 \cdot \ s/g=t_{1}^2 - t_{1}^2 + 2 \cdot \ t \cdot \ t_{1} - t^2 \ \\ 2 \cdot \ s/g + t^2=2 \cdot \ t \cdot \ t_{1} \ \\ \ \\ t_{1}=\dfrac{ t^2 + 2 \cdot \ s/g }{ 2 \cdot \ t }=\dfrac{ 0.5^2 + 2 \cdot \ 10/10 }{ 2 \cdot \ 0.5 }=\dfrac{ 9 }{ 4 }=2.25 \ \text{s} \ \\ \ \\ v=g \cdot \ t_{1}=10 \cdot \ 2.25=\dfrac{ 45 }{ 2 }=22.5 \ \text{m/s}$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Do you want to convert velocity (speed) units?
Do you want to convert time units like minutes to seconds?

## Next similar math problems:

1. Free fall
How long does the stone fall freely into a depth of 80m? What speed will it hit the bottom of the abyss?
2. 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)
3. 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
4. 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)
5. Car overtaking
A passenger car travels at a speed of 30 m/s, and before it travels freight truck that drives at a constant speed of 10 m/s. Within 30 meters of the truck, the driver of the car finds out that the truck can not overtake. That's why it starts braking with
6. G forces
Calculate deceleration of car (as multiple of gravitational acceleration g = 9.81 m/s2) which occurs when a car in a frontal collision slows down uniformly from a speed 111 km/h to 0 km/h in 1.2 meters trajectory.
7. Brakes of a car
For the brakes of a passenger car to be effective, it is prescribed that a car moving on a horizontal road at a speed of 40 km. A car must stop on the track 15.4 m. What is the deceleration of the car?
8. 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?
9. Driver
The driver of the car at a speed of 100 km/h faced the obstacle and began to brake with a slowing of 5 m/s². What is the path to stopping the car when the driver has registered the obstacle with a delay of 0.7 s?
10. Acceleration
The car accelerates at rate 0.5m/s2. How long travels 400 meters and what will be its speed?
11. Abyss
Stone was pushed into the abyss: 2 seconds after we heard hitting the 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)
12. Znojmo
From Znojmo to Brno started truck with a trailer at an average speed 53 km per hour. Against him 14 minutes later from Brno started car with an average speed of 1.2-times greater than the truck. How long and how far from Znojmo, they meet if the distan
13. Wavelength
Calculate the wavelength of the tone frequency 11 kHz if the sound travels at speeds of 343 m/s.
14. A particle
A particle moves in a straight line so that its velocity (m/s) at time t seconds is given by v(t) = 3t2-4t-4, t>0. Initially the particle is 8 meters to the right of a fixed origin. After how many seconds is the particle at the origin?
15. Cyclist vs car
Cyclist rode out of the city at 18 km/h. 1 hour 30 minutes behind him started car and caught up with the cyclist in 50 minutes. How fast was driving the car? Where (what kilometer) from the city car overtook a cyclist?
16. Train 2
The train slowed down from 90 km/h to 72 km/h in 5 seconds. How long track travel?
17. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?