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A ball is rolled off a horizontal tabletop so that it leaves the tabletop and takes 0.35 seconds to reach the ground. The ball lands 0.75 meters horizontally from the base of the table.
a. Determine the horizontal velocity of the ball.
b. Determine the height of the table.

Respuesta :

kinematics allows to find the kinetic variables and the relationships between position, speed and acceleration, for launching projectiles we can find:

a)  The horizontal velocity  vₓ = 2.1 m/s

b) The height of the table y₀= 0.60 m

given parameters

  • Time to reach the floor t = 0.35 s
  • Horizontal distance x = 0.75 m

to find

   a. Horizontal speed

   b. table height

Let's use the kinematics relations, let's start by defining a reference frame with the x-axis along the motion of the ball and the vertical y-axis with the positive direction up.

We look for the initial velocity in the x axis, there is no acceleration we can use the uniform kinematic relations

         vₓ = x / t

Where vx is the horizontal velocity, g the acceleration of gravity (g=9.8 m/s²) and t the time

         vₓ = 0.75 / 0.35

         vₓ = 2.14 m / s

We look for the height of the table that corresponds to the initial height (y₀) of the ball, when reaching the floor the height is zero, on the vertical axis the initial velocity is zero (v_{oy} = 0)

        y = y₀ + v_{oy} t - ½ g t²

        0 = y₀ + 0 - ½ g t²

        y₀ = ½ g t²

        y₀ = ½ 9.8 0.35²

        y₀i = 0.60 m

  • In conclusion with the kinematic relations for the launch of projectiles we can find the horizontal velocity vₓ = 2.1 m / s and the height of the table i = 0.60 m

learn more about projectile launch here:

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