Question

A physics teacher is designing a ballistics event for a science competition. The ceiling is 3.00m high, and the maximum velocity of the projectile will be 20m/s.
What is the maximum that the vertical component of the projectiles initial velocity could have?

Answer 1

The launch proyectiles of kinematics  allows to find the maximum initial vertical velocity of the body so that it just reaches the ceiling

             v_{oy} = 2.56 m / s

       

Given parameters

• The ceiling height y = 3 m

To find

• Maximum vertical speed

Projectile launching is an application of kinematics where on the x axis there is no acceleration or and on the y axis the acceleration is the acceleration of gravity (g = 9.8 m / s ^ 2)

In this case, the maximum vertical velocity that the body can have occurs when the velocity on the ceiling is zero.

            v_y² = v_{oy}² - 2 g y

where v and v_{oy} are the initial velocity at the ceiling e initial, respectively, g the acceleration of gravity e and the height

           0 = v_{oy}² - 2 g y

           v_{oy} = $\sqrt{2gy}$

           v_{oy} = $\sqrt{2 \ 9.8 \ 3}$

           v_{oy} = 2.56 m / s

In conclusion with the kinematic of launch projectiles we can find the maximum initial vertical velocity of the body so that it just reaches the ceiling

             v_{oy} = 2.56 m / s

learn more about projectile launch here:

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