Respuesta :
Answer:
The horizontal distance d does the ball travel before landing is 1.72 m.
Explanation:
Given that,
Height of ramp [tex]h_{1}=2.30\ m[/tex]
Height of bottom of ramp [tex]h_{2}=1.69\ m[/tex]
Diameter = 0.17 m
Suppose we need to calculate the horizontal distance d does the ball travel before landing?
We need to calculate the time
Using equation of motion
[tex]h_{2}=ut+\dfrac{1}{2}gt^2[/tex]
[tex]t=\sqrt{\dfrac{2h_{2}}{g}}[/tex]
[tex]t=\sqrt{\dfrac{2\times1.69}{9.8}}[/tex]
[tex]t=0.587\ sec[/tex]
We need to calculate the velocity of the ball
Using formula of kinetic energy
[tex]K.E=\dfrac{1}{2}mv^2+\dfrac{1}{2}I\omega^2[/tex]
[tex]K.E=\dfrac{1}{2}mv^2+\dfrac{1}{2}\times(\dfrac{2}{5}mr^2)\times(\dfrac{v}{r})^2[/tex]
[tex]K.E=\dfrac{7}{10}mv^2[/tex]
Using conservation of energy
[tex]K.E=mg(h_{1}-h_{2})[/tex]
[tex]\dfrac{7}{10}mv^2=mg(h_{1}-h_{2})[/tex]
[tex]v^2=\dfrac{10}{7}\times g(h_{1}-h_{2})[/tex]
Put the value into the formula
[tex]v=\sqrt{\dfrac{10\times9.8\times(2.30-1.69)}{7}}[/tex]
[tex]v=2.922\ m/s[/tex]
We need to calculate the horizontal distance d does the ball travel before landing
Using formula of distance
[tex]d =vt[/tex]
Where. d = distance
t = time
v = velocity
Put the value into the formula
[tex]d=2.922\times 0.587[/tex]
[tex]d=1.72\ m[/tex]
Hence, The horizontal distance d does the ball travel before landing is 1.72 m.
