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)

Result

t =  4 s
x =  60 m

Solution:

$h=80 \ \text{m} \ \\ g=10 \ \text{m/s}^2 \ \\ v_{0}=15 \ \text{m/s} \ \\ \ \\ h=\dfrac{ 1 }{ 2 } \cdot \ g t^2 \ \\ \ \\ t=\sqrt{ 2 \cdot \ h/g }=\sqrt{ 2 \cdot \ 80/10 }=4 \ \text{s}$

$x=v_{0} \cdot \ t=15 \cdot \ 4=60 \ \text{m}$

Try another example

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

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. 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.
2. 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
3. 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)
4. 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
5. 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?
6. 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?
7. Free fall
   How long does the stone fall freely into a depth of 80m? What speed will it hit the bottom of the abyss?
8. Train 2
   The train slowed down from 90 km/h to 72 km/h in 5 seconds. How long track travel?
9. Acceleration
   The car accelerates at rate 0.5m/s². How long travels 400 meters and what will be its speed?
10. 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?
11. Free fall
    The free fall body has gone 10m in the last 0.5s. Find the body speed at the moment of impact.
12. Rocket start
    The body launched vertically up returns to the start site in 6 seconds. What height did it have?
13. 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?
14. 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?
15. Wavelength
    Calculate the wavelength of the tone frequency 11 kHz if the sound travels at speeds of 343 m/s.
16. 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
17. The tram
    The tram is moving with acceleration a = 0.3m/s2. How long it will pass the first meter of track? How long does it take 10 meters. What is its speed at the end of the 10 meters track?