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 s s=10 m  g=10 m/s2    s=12 g t1212 g (t1t)2 2 s/g=t12(t1t)2 2 s/g=t12t12+2 t t1t2 2 s/g+t2=2 t t1  t1=t2+2 s/g2 t=0.52+2 10/102 0.5=94=2.25 s  v=g t1=10 2.25=452=22.5 m/st=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...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




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

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Free fall
    volny pad How long does the stone fall freely into a depth of 80m? What speed will it hit the bottom of the abyss?
  2. Bomber
    tu-160 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
    motion2_4 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
    vodorovny_vrh 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. Rocket start
    freefall1 The body launched vertically up returns to the start site in 6 seconds. What height did it have?
  6. Car overtaking
    crash_2 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
  7. G forces
    car_crash 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.
  8. Acceleration
    caR The car accelerates at rate 0.5m/s2. How long travels 400 meters and what will be its speed?
  9. Driver
    cargo_truck_4 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. Brakes
    pneu 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?
  11. Abyss
    Mountain 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. Wavelength
    wave_length Calculate the wavelength of the tone frequency 11 kHz if the sound travels at speeds of 343 m/s.
  13. Pre účinnosť
    motion2_6 Pre účinnosť bŕzd osobného vozidla je predpísané, že automobil pohybujúci sa po vodorovnej vozovke rýchlosťou 40km. H musí zastaviť na dráhe 15,4 m. Aké veľké je pritom spomalenie automobilu?
  14. Cyclist vs car
    car2 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?
  15. Train 2
    zssk_vlak The train slowed down from 90 km/h to 72 km/h in 5 seconds. How long track travel?
  16. Circular motion
    mass_point_circle Mass point moves moves uniformly in a circle with radius r = 3.4 m angular velocity ω = 3.6 rad/s. Calculate the period, frequency, and the centripetal acceleration of this movement.
  17. Theorem prove
    thales_1 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?