Question

a particle is projected with a particular speed up the inclined plane of inclination 20 degree with the horizontal the angle of projection with the inclined place at which range on the inclined plane is maximum

Answer 1

The angle of projection with the inclined plane at which the range on the inclined plane is maximum is 70°.

Step-by-step explanation:

The angle of projection with the inclined plane at which the range on the inclined plane is maximum can be determined using the concept of projectile motion. The range of a projectile on level ground launched at an angle above the horizontal with initial speed vo is given by R = vo^2 * sin(2theta) / g, where vo is the initial speed, theta is the angle of projection, and g is the acceleration due to gravity.

For the inclined plane, we need to break the initial velocity into its horizontal and vertical components. The vertical component of the initial velocity is v0 * sin(20°) and the horizontal component is v0 * cos(20°). The angle of projection with the inclined plane at which the range is maximum is the angle at which the vertical component of the velocity is zero. In this case, when v0 * sin(20°) = 0, which occurs when the angle of projection with the inclined plane is 90° - 20° = 70°.

Answer 2

The angle of projection at which the range on the inclined plane is maximum is 45 degrees.

Step-by-step explanation:

The angle of projection at which the range on the inclined plane is maximum can be determined using the concept of projectile motion. The range of a projectile is maximum when the angle of projection is 45 degrees, assuming no air resistance. This means that if a particle is projected with a particular speed up the inclined plane of inclination 20 degrees with the horizontal, the angle of projection with the inclined plane at which the range is maximum would be 45 degrees.