Question

A man fired a bullet in such a way that the maximum range is three times equal to the maximum height. Find the angle at which he wants to fire the bullet?​

Answer 1

Step-by-step explanation:

We can solve this problem using the equations of projectile motion. The maximum range and maximum height of a projectile are given by:

R = (v^2/g) * sin(2theta)

H = (v^2/2g) * sin^2(theta)

where v is the initial velocity of the bullet, g is the acceleration due to gravity, and theta is the angle at which the bullet is fired.

From the problem statement, we are given that R = 3H. Substituting this into the equations above, we get:

3H = (v^2/g) * sin(2theta)

H = (v^2/2g) * sin^2(theta)

Dividing the first equation by the second equation and simplifying, we get:

tan(2theta) = 6

Using a calculator, we can find that the angle whose tangent is 6 is approximately 80.5 degrees. Therefore, the man should fire the bullet at an angle of approximately 40.25 degrees (since the maximum range occurs at twice this angle).