Throwing a dart from a roof - Velocity

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In summary, a dart is thrown horizontally from a building's rooftop with a time of flight of 2.0 seconds. It sticks in the ground at a 53.1 degree angle with the ground. To find the initial speed, the equation of motion is used with a final vertical velocity of 19.6 m/s and a horizontal component of 14.7 m/s. The final answer is 14.7 m/s.
  • #1
mybrohshi5
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Homework Statement



A dart is thrown horizontally from a buildings rooftop. The dart's time of flight is 2.0 s. The dart sticks in the ground such that it makes a 53.1 degree angle with the ground.

With what speed was the dart thrown?

The Attempt at a Solution



I am studying for my final and i do not get this problem from one of my previous tests.

The answer is 14.7 m/s and i have no idea how to get it. Can anyone point me in the right direction.

Thank you :)
 
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  • #2
Well if it is throw horizontally, then the initial vertical velocity is zero right? Using an equation of motion, what would be final vertical velocity when t=2?
 
  • #3
Is the final vertical velocity when t=2 just 19.6 m/s

I got that from

Vf = Vi + at

oh so then from that the x component of the Vf will be the same as the velocity initial correct?

so

tan(53.1) = 19.6 / Vfx

Vfx = 14.7 m/s

Does that seem right?
 
  • #4
Yes that looks correct.
 
  • #5
Yay! thank you very much :)
 

1. What is the initial velocity of a dart when thrown from a roof?

The initial velocity of a dart thrown from a roof depends on a variety of factors, including the angle of release and the height of the roof. Generally, the initial velocity can range from 5 to 20 meters per second.

2. How does the angle of release affect the velocity of a dart thrown from a roof?

The angle of release plays a crucial role in determining the velocity of a dart thrown from a roof. A higher angle of release will result in a higher initial velocity, while a lower angle of release will result in a lower initial velocity.

3. Can the velocity of a dart thrown from a roof be calculated using a formula?

Yes, the velocity of a dart can be calculated using the formula v = √(2gh), where g is the acceleration due to gravity and h is the height of the roof. However, this formula assumes ideal conditions and may not accurately reflect the actual velocity of the dart.

4. How does air resistance affect the velocity of a dart thrown from a roof?

Air resistance can significantly affect the velocity of a dart thrown from a roof. As the dart travels through the air, it experiences drag, which slows it down. The higher the velocity of the dart, the greater the effect of air resistance.

5. What other factors can affect the velocity of a dart thrown from a roof?

Aside from the angle of release, height of the roof, and air resistance, other factors that can affect the velocity of a dart thrown from a roof include the weight and shape of the dart, as well as any external forces acting on it, such as wind or obstacles in its path.

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