Mechanical Engineering - Engineering Mechanics - Discussion

I think they will be of the same values even if the plane that is being his is inclined up or down. They will his only a particular point with respect to horizontal distance (i.e. Range).

But the height of impact will change depending on the inclination. Agree. ?

When projectile moves upward its velocity reduce because negative gravitational acceleration there for time increase to reach same height but time taken to reach the ground less due to ground. And distance (range) = v/t.

As t increases d reduce &t reduce d increase. There for distance (range) inversely proportional to time.

I think only velocity changes but not range. Distance remains same.

It is so because work is done align with the action of gravity.

While moving upward gravitational force restricts the motion of the body on the other hand, while moving downward gravitational force help the body to move downward.

So with force range of projectile (body projected at a target with particular force, force for both upward and downward motion is same) increases.

In case of downward direction gravity helps to velocity weather the upward direction gravitational force opposes the moving velocity.

That's why the range of projectile on a downward inclined plane is MORE THAN the range on upward inclined plane for the same velocity of projection and angle of projection.

This can be easily explained with diagrams.

It's quite obvious that when the ANGLE OF PROJECTION IS SAME, the range of the projectile is more when the inclination is downwards than when the inclination is upwards.

The upwards inclination already reduces the distance the body can travel when projected as compared to a downwards inclination.

Just employ imagination and diagrams. Better still, try it out on a hill.

The range of projectile on downward inclination is always less than the range of projectile in upward inclination plane in general (you can observe the same by throwing a ball in the air).

And the angle of projection of downward inclined projectile is always greater compared to upward one. Now as per condition of the statement given in question VELOCITY AND ANGLE OF PROJECTION MUST BE SAME IN BOTH UPWARD AND DOWNWARD INCLINATION. In the hypothetical condition in which angle of inclination is same the range of downward projectile need to be increased and it becomes greater than the range of the upward projectile.

I Guess the Range of the projectile depends on the angle of the upward and downward inclination.

If they have the same inclination angle, the range of the would be same. If there is the difference in their angle, then the range of the projectile will also be affected. What do you say?

Gravity helps to increase speed in downward direction.