When landing at the same height as the initial velocity;
the time to apogee is equal to the time from apogee,
the initial velocity is equal to the negative of the final velocity,
the distance to apogee is equal to the distance from apogee.
More Concepts to Help Define the Givens
When a projectile lands at the same height it is launched from the initial velocity is equal in magnitude to the impact velocity and in the opposite direction.
The two pulsating projectiles have equal and opposite velocities. For a problem where the projectile lands at the same height it is launched from
The launch velocity is equal and opposite to the impact velocity.
The time from the ground up to apogee is equal to the time from apogee to the ground.
The distance from the ground to apogee is equal to the distance from apogee to the ground.
When solving for the total time of flight from launch to impact, the displacement Δx = 0. (This is because it lands at the same height it is launched from.
In terms of the list of givens this means that the the magnitude of vimpact = –vo.
It also means when finding the time to apogee, the problem could be reversed and the projectile could be dropped from apogee. This could be handy because it would make the initial velocity equal to zero.
Initial Velocities that are Horizontal
Some projectile problems involve a ball rolling off a ledge horizontally.
In this situation the horizontal component of the initial velocity is the same as the initial velocity. The vertical initial velocity is zero. In the steps outlined earlier, skip step number one -where a triangle is drawn. The data table for the animation above would look like the one below.
Example 9 ...What to do when Vo is horizontal
A dog runs horizontally off a ledge 3.00 m above a pond. The dog was running at 6.00 m/s. How far away from the edge of the ledge did the dog land? (Looking for the range.)
by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)