These are known as balanced forces because they will not change the motion of the object, and it will remain at rest unless forces become unbalanced- meaning they would be unequal and not opposing.
Average velocity is change in position over the change in time. You have to take the directions into account. 100km east and then 100km south. That forms a right triangle, so you can use Pythagorean's theorem to find the hypotenuse which would be the displacement from his initial position:
Now take the displacement and divide it by the time it took to do the trip, 3 hours:
Once in the air, no forces act on the froghopper, so it keeps moving with the same initial horizontal speed.
This horizontal component, is the projection of the velocity vector on the horizontal direction (x-axis):
The horizontal displacement can be simply calculated as follows:
Vertical movement:
As the vertical and horizontal are independent each other (due to they are perpendicular, so there is no projection of one movement on the other), in the vertical direction, all happens as if would be a body thrown upward with a given initial vertical velocity.
This velocity can be found as the projection of the velocity vector on the vertical direction (y-axis):
Once in the air, the gravity will cause that the froghopper be slow down, till it reaches to the maximum height, where it will come momentarily to an stop.
In that moment, we can apply the following kinematic equation:
where vfy = 0, g = -9.8m/s2, hmax = 52.7 cm= 0.527 m
Replacing by the givens, we can solve for voy:
From the equation (1), we can solve for the magnitude of the initial velocity, v₀:
B)
With the value of the magnitude of the initial velocity, we can find the horizontal component vox, as follows:
In order to know the horizontal distance travelled, we need to find the time that the insect was in the air.
We can use the equation for the vertical displacement, replacing this value by 0, as follows:
Replacing by the givens, and rearranging terms, we can solve for t:
Finally, we find the horizontal displacement, as follows:
The horizontal distance covered by the froghopper was 1.33 m.
