How high will the projectile be at 5 km downrange?

In summary, a projectile is fired with an initial speed of 500 m/s at an angle of elevation of 45°. The flight time is 72.2 seconds and it will travel 25526.6 meters. To find the height when the projectile is 5 km downrange, the equation r(t)=x+(y-\frac{1}{2}gt2) can be used but the time calculated earlier needs to be substituted in.
  • #1
jdawg
367
2

Homework Statement



A projectile is fired with an initial speed of 500 m/s at an angle of elevation of 45°. When and how far away will the projectile strike? How high overhead will the projectile be when it is 5 km downrange?

Homework Equations





The Attempt at a Solution


Flight time: t=[itex]\frac{2(500)sin45°}{9.8}[/itex]
t=72.2 sec
How far: x=500cos45°(72.2)
x=25526.6 m

I'm not entirely sure how to figure out the second part though. I was thinking about using this formula: r(t)=vocosθ(t)+(vosinθ(t)-[itex]\frac{1}{2}[/itex]gt2)
r(t)=x+(y-[itex]\frac{1}{2}[/itex]gt2)
Am I on the right track with this? Do I use the t I calculated earlier for this equation?
 
Last edited:
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  • #2
How long will it take to be that far down range?
 

1. What is the relationship between flight time and height?

The relationship between flight time and height is a direct one. As the height increases, the flight time also increases. This is because a higher height allows for a longer distance to be covered, resulting in a longer flight time.

2. How does air resistance affect flight time and height?

Air resistance plays a significant role in affecting flight time and height. It acts as a counterforce to the motion of the object, reducing its speed and therefore limiting the height and flight time. Objects with less air resistance, such as a streamlined airplane, can reach higher heights and have longer flight times compared to objects with more air resistance, such as a feather.

3. Can flight time and height be calculated accurately?

Yes, flight time and height can be calculated accurately using the laws of physics and mathematical equations, such as the equations of motion. However, factors such as air resistance, wind, and air density can affect the accuracy of these calculations.

4. What is the maximum height and flight time achievable by an object?

The maximum height and flight time achievable by an object depend on various factors, including the initial velocity, air resistance, and gravitational force. In a vacuum, where there is no air resistance, the maximum height and flight time would be infinite. However, in real-world scenarios, the maximum height and flight time are limited by factors such as air resistance and gravity.

5. How can flight time and height be improved for airplanes?

There are several ways to improve flight time and height for airplanes. One way is to reduce air resistance by designing a more streamlined and aerodynamic shape for the airplane. Another way is to increase the initial velocity of the airplane, which can be achieved through more powerful engines or using a runway with a slope. Additionally, adjusting the angle of the airplane's wings can also affect the flight time and height achieved.

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