As elastic potential energy is transferred into kinetic energy and the projectile leaves the arm of the catapult at an initial velocity, it begins to travel on its parabolic path, like any projectile launched at an angle; as the negative acceleration of gravity brings it to a peak point, it proceeds to pull the projectile back down to earth.
Horizontal and Vertical Components
In order to examine the motion of the projectile, we must individually look at its components and therefore, we must break down the initial velocity into horizontal and vertical components.
Let's now compile all of our known values for each component.
Horizontal Component
|
Vertical Component
| ||
Initial velocity
|
7.63 m/s
|
Initial velocity
|
2.78m/s
|
Acceleration
|
0 m/s2
|
Acceleration
|
–9.8 m/s2
|
Time
|
?
|
Time
|
?
|
Displacement
|
?
|
Displacement
|
–0.44 m
|
- The displacement in the vertical component is negative since the projectile leaves a point above the ground.
Time In the Air
Next, we can solve for time in the vertical component.
Since we are dealing with a quadratic, we are given two variable values as an answer. Since one of the values is negative, we can deem it incorrect since time cannot have a negative value. We can also sketch the parabolic path of the parabola to understand where the second answer (-0.129s) comes from.
If we were to continue to sketch the path of the projectile's motion before it is launched from its height of 0.44m, we would eventually reach an imaginary point at which the displacement is -0.44m. This is the imaginary point that the projectile would reach in -0.129s.
Distance Traveled
Upon finding the time the projectile will spend in the air, we can use this same time value to find the displacement in the horizontal direction (distance traveled).
