A small steel ball bearing with a mass of 19.0 g is on a short compressed spring. When aimed vertically and suddenly released, the spring sends the bearing to a height of 1.35 m. Calculate the horizontal distance the ball would travel if the same spring were aimed 35.0 deg from the horizontal?

Respuesta :

Answer:

[tex]R_{horizontal}=2.53\ m[/tex]

Explanation:

Given,

Mass of the steel = 19 g

height reached, h = 1.35 m

angle, θ = 35°

when the ball is projected vertically with initial velocity v.

Maximum height reached is equal to,[tex]h = \dfrac{v^2}{2g}[/tex]

initial velocity,

[tex]v=\sqrt{2gh}[/tex]

[tex]v=\sqrt{2\times 9.8\times 1.35}[/tex]

  v = 5.14 m/s

Hence , the maximum velocity is equal to 5.14 m/s

For projectile motion horizontal distance is given by

[tex]R_{horizontal}=\dfrac{v^2sin 2\theta}{g}[/tex]

[tex]R_{horizontal}=\dfrac{5.14^2sin (2\times 35^{\circ}}{9.8}[/tex]

[tex]R_{horizontal}=2.53\ m[/tex]

the horizontal distance travel by the ball is equal to [tex]R_{horizontal}=2.53\ m[/tex]