Projectile problem -- How much to increase Vi to reach a farther target?

In summary, the missile gains a 50% increase in velocity when it is required to hit a target at a horizontal distance of 675 km launched at the same angle with the horizontal.
  • #1
D.Man Hazarika
7
0

Homework Statement


A missile is launched from the ground making 45 degree with the horizontal to hit a target at a horizontal distance of 300 km. If it is required to hit a target at a horizontal distance of 675 km launched at same angle with horizontal, find the percentage change in its velocity of projection. (Answer is 50% increase)

Homework Equations

The Attempt at a Solution


I did it like this but I got 44.5% whereas the answer is 50%

So I did it like this...
R= u²sin2∅/g
I put R= 300km and 675km in the given formula in two equations...
I got √100/3 and √75
Therefore to find % increase
√100/3 divided by √75 * 100
I got 44.5%
But the answer is 50%...please help
 
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  • #2
D.Man Hazarika said:

Homework Statement


A missile is launched from the ground making 45 degree with the horizontal to hit a target at a horizontal distance of 300 km. If it is required to hit a target at a horizontal distance of 675 km launched at same angle with horizontal, find the percentage change in its velocity of projection. (Answer is 50% increase)

Homework Equations

The Attempt at a Solution


I did it like this but I got 44.5% whereas the answer is 50%

So I did it like this...
R= u²sin2∅/g
I put R= 300km and 675km in the given formula in two equations...
I got √100/3 and √75
Therefore to find % increase
√100/3 divided by √75 * 100
I got 44.5%
But the answer is 50%...please help

Such ranges and launch angles usually suggest that the rocket gains a relatively large altitude before hitting its target. Your range formula assumes that g is constant, which is OK for problems where the projectile remains close to the surface of the earth. For projectiles which travel high in the atmosphere, I'm sure this formula must be modified.

The variation of g with altitude is discussed in this article:

http://en.wikipedia.org/wiki/Gravity_of_Earth

This might be the source of the discrepancy of your calculation with the answer key.
 
  • #3
Look I am confused I just need u to show me the steps of doing this sum...
 
  • #4
SteamKing said:
This might be the source of the discrepancy of your calculation with the answer key.
No, it's just numerical error.
D.Man Hazarika said:
I got √100/3 and √75
I don't understand how you got those. Please post all steps.
 
  • #5
OK thanks anyways I got the answer
 

Related to Projectile problem -- How much to increase Vi to reach a farther target?

1. How does the initial velocity affect the distance a projectile can reach?

The initial velocity (Vi) plays a crucial role in determining the distance a projectile can reach. The higher the initial velocity, the farther the projectile will travel. This is because the initial velocity provides the initial push for the projectile, and the greater the push, the farther it will go before gravity pulls it back down.

2. Is there a specific formula to calculate how much to increase Vi to reach a farther target?

Yes, there is a formula known as the range equation that can be used to calculate the increase in initial velocity needed to reach a farther target. This equation takes into account the initial velocity, launch angle, and gravitational acceleration to determine the maximum distance a projectile can travel.

3. Can the angle of launch affect the required increase in Vi to reach a farther target?

Yes, the angle of launch can affect the required increase in Vi to reach a farther target. Generally, a lower launch angle (closer to the horizontal) will require a larger increase in Vi compared to a higher launch angle (closer to the vertical). This is because a lower launch angle results in a shorter flight time and less time for the projectile to cover a greater distance.

4. Are there any other factors besides Vi that can impact the distance a projectile can reach?

Yes, there are other factors that can affect the distance a projectile can reach, such as air resistance, wind speed and direction, and the mass and shape of the projectile. These factors can cause variations in the trajectory of the projectile, and thus, may require adjustments to the initial velocity to reach a farther target.

5. Is there a limit to how much Vi can be increased to reach a farther target?

There is no specific limit to how much Vi can be increased to reach a farther target. However, it is important to consider the physical limitations of the projectile and the launching mechanism. Increasing the initial velocity too much may cause the projectile to break or the launching mechanism to malfunction. It is also important to consider safety precautions and any regulations that may limit the maximum velocity of a projectile.

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