Question

A and B are two bullets fired with velocity 1km/h and 2km/h. Find the ratio of the maximum range covered by these bullets?

Answer 1

Answer:

So the Ratio of max ranges covered is 1:4

Solution:

The formula for finding the range of the projectile is

R $=\frac{v^{2}*sin*2(theeta)}{g}$

Now Range will be maximum

when theeta = 45°

and

sin 2Ф = sin 90 = 1

so range becomes

R $=\frac{v^{2}}{g}$

Now for bullet 1

v1 = 1 km/h = (1*1000)/3600 = 10/36

v2 = 2km/h = (2*1000)/3600 = 20/36

Now

R1 $=\frac{v1^{2}}{g}$

Putting the value

R1 $=\frac{10^{2}}{36^{2}*g}$

R2$=\frac{20^{2}}{36^{2}*g}$

Now ratio of these two are and cancelling out the similar terms

R1 : R2

$10^{2}:20^{2}$

it is

100 : 400

dividing both sides by 100

it is

1:4

So the Ratio of max ranges covered is 1:4