For a given launch velocity, at which launch angle does the projectile undergo the maximum horizontal displacement?

For a given launch velocity, the smaller the angle the greater the hor.

displacement Dx max occurs at 0 deg.

90

45 degrees

To determine at which launch angle the projectile undergoes the maximum horizontal displacement, we can use the concept of projectile motion and analyze how the range (horizontal displacement) varies with different launch angles.

The range of a projectile refers to the horizontal distance it travels before hitting the ground. The range is affected by the initial velocity of the projectile and the launch angle. In general, the range is maximized when the launch angle is 45 degrees.

To understand why, we need to consider the horizontal and vertical components of the initial velocity separately. The initial velocity can be split into its horizontal component (Vx) and vertical component (Vy). The horizontal component remains constant throughout the motion, while the vertical component changes due to the effect of gravity.

At a launch angle of 45 degrees, the initial velocity is split equally between the horizontal and vertical components: Vx = Vy = V * cos(45) = V / sqrt(2), where V is the launch velocity.

The time taken for the projectile to reach its maximum height is given by t = Vy / g, where g is the acceleration due to gravity. At the maximum height, the vertical velocity Vy becomes zero.

Since the time taken to reach the maximum height is the same as the time taken to fall back to the ground, the total time of flight can be calculated as T = 2 * t = 2 * Vy / g.

Using this total time of flight, we can calculate the range (R) of the projectile:

R = Vx * T = (V / sqrt(2)) * (2 * Vy / g) = (V^2 * sin(90) / g,

where sin(90) equals 1 because the angles are measured with respect to the horizontal axis.

From this equation, we can see that the range R depends on the square of the launch velocity (V^2) and the reciprocal of the acceleration due to gravity (1/g). It does not depend on the launch angle.

Therefore, the range (horizontal displacement) is maximized when other factors, such as launch velocity, remain constant, and the launch angle is 45 degrees.

hi

i
really
dont
know