Height of a building with a Projectile

In summary, a ball is launched from the top of a building at an angle of 38° and a speed of 16m/s. After 45 seconds, it hits the ground and the height of the building is asked. Using the equation Δy=VyiΔt+1/2gΔtsquared, the answer of 9480m is obtained. However, there seems to be a discrepancy in the calculations as the building cannot be that high and the vertical velocity after 1 second would exceed the speed of sound. It is important to check for errors and consider air resistance when solving such problems.
  • #1
guma671
3
0

Homework Statement



A ball is launched at an angle of 38° at 16m/s off of the top of a building, the ball finally hits the ground after 45seconds. What is the height of the building? Gravity is normal 9.80m.s squared. The answer to the problem is 9480m.

Homework Equations



I just needed a starting point. I wasn't sure really where to go with the problem.

The Attempt at a Solution



First i tried to find Vy by 16.0m/s * sin(38°) and got a value of 4.741m/s. I then plugged it into the equation Δy=VyiΔt+1/2gΔtsquared but the answer came out to around 10,000.
 
Physics news on Phys.org
  • #2
Why don't you show your complete calculations?
 
  • #3
what do you mean?
 
  • #4
oh well with the answer i got around 10,000 it was just Y=(16m/s)(45s)+1/2(-9.8)(45)squared which came out to -9202.5
 
  • #5
Always good to check things.
1. You know sin(30°) = 0.5 so you should expect Vy > 8 m/s !
2. If even that leads to an improbable answer, check that you read the OP correctly. Perhaps it says 4.5 seconds ?
 
  • #6
Posts crossed. I am a slow typer. Now you use Vo, not Vy. Not that it matters much on a 10000 m scale. But it does on a 100 m scale.
 
  • #7
Come again. What building is 9480 m high ?
 
  • #8
If the 9480 m is in the answer book, you may have to deal with a case of sloppy re-use of old exercises. They change a number but don't bother to check if it's sensible. In this case that is double painful: the 9480 is nonsense and on top of that, after 1 second, the vertical component of the velocity is 0. In the 44 seconds after that it would go -430 m/s, way over the speed of sound. If the building is on Earth (9.8 m/s^2), the air restance can't be ignored anymore, even for a lead ball.
 

1. What is the concept behind measuring the height of a building using a projectile?

The concept is to use the principles of projectile motion to calculate the height of a building by measuring the time it takes for an object to fall from the top of the building to the ground.

2. What is the equation used to calculate the height of a building with a projectile?

The equation used is h = (1/2)gt^2, where h is the height of the building, g is the acceleration due to gravity (9.8 m/s^2), and t is the time it takes for the object to fall.

3. How accurate is this method of measuring the height of a building?

This method can be fairly accurate if the measurements are taken correctly and the projectile is launched at a consistent speed. However, external factors such as wind resistance and air density can affect the accuracy of the calculation.

4. Can this method be used for all types of buildings?

This method can be used for most types of buildings, as long as there is a clear and unobstructed path for the projectile to fall. It may not be suitable for buildings with irregular shapes or structures that may interfere with the trajectory of the projectile.

5. Are there any safety precautions that need to be taken when measuring the height of a building with a projectile?

Yes, it is important to ensure the safety of yourself and others when launching a projectile, especially in urban areas. It is recommended to use a small and lightweight object, and to launch it at a low angle to minimize the risk of injury or damage.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
14
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
2
Replies
39
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
781
  • Introductory Physics Homework Help
Replies
5
Views
807
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
15
Views
20K
Back
Top