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

1. Jan 27, 2015

### D.Man Hazarika

1. The problem statement, all variables and given/known data
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)

2. Relevant equations

3. 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%

2. Jan 27, 2015

### SteamKing

Staff Emeritus
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.

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

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

3. Jan 27, 2015

### D.Man Hazarika

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

4. Jan 27, 2015

### haruspex

No, it's just numerical error.
I don't understand how you got those. Please post all steps.

5. Jan 28, 2015

### D.Man Hazarika

OK thanks anyways I got the answer