# Projectile Motion on an Inclined Plane

Let a particle be projected up with a speed

*u*from an inclined plane which makes an angle Î± with the horizontal velocity of projection and makes an angle*Î¸*with the inclined plane.We have taken reference

*x*-axis in the direction of plane (Fig. 11). Hence, the components of initial velocity parallel and perpendicular to the plane are equal to*u*cos*Î¸*and*u*sin*Î¸*, respectively, i.e.,*and**u*_{âŠ¥}=*u*sin*Î¸*.**Fig. 11**

The component of

*g*along the plane is*g*sin Î± and perpendicular to the plane is*g*cos Î± as shown in Fig. 11, i.e., and*a*_{âŠ¥}=*g*cos Î±. Therefore, the particle decelerates at a rate of*g*sin Î± as it moves from*O*to*P*.# Time of flight

We know for oblique projectile motion,

or we can say
âˆ´ Time of flight on an inclined plane

# Maximum height

We know for oblique projectile motion,

or we can say

âˆ´ Maximum height on an inclined plane

# Horizontal range

- Maximum range occurs when
- The maximum range along the inclined plane when the projectile is thrown upward is given by
- The maximum range along the inclined plane when the projectile is thrown downward is given by