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

[D.Man Hazarika]

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

 

[SteamKing]

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.

 

[D.Man Hazarika]

Look I am confused I just need u to show me the steps of doing this sum...

 

[haruspex]

This might be the source of the discrepancy of your calculation with the answer key.

No, it's just numerical error.

I got √100/3 and √75

I don't understand how you got those. Please post all steps.

 

[D.Man Hazarika]

OK thanks anyways I got the answer