Respuesta :
Answer:
(a). The horizontal velocity is 1.46 m/s.
(b). The direction of the mug's velocity just before it hit the floor is 74.7° below the horizontal.
Explanation:
Given that,
Height of the counter = 1.46 m
Distance = 0.80 m
We need to calculate the time
Using equation of motion
[tex]s_{y}=ut+\dfrac{1}{2}gt^2[/tex]
[tex]s_{y}=\dfrac{1}{2}gt^2[/tex]
Put the value into the formula
[tex]1.46=\dfrac{1}{2}\times9.8\times t^2[/tex]
[tex]t^2=\dfrac{1.46\times 2}{9.8}[/tex]
[tex]t=\sqrt{\dfrac{1.46\times2}{9.8}}[/tex]
[tex]t=0.545\ sec[/tex]
Here, horizontal velocity is constant
(a). We need to calculate the velocity
Using formula of velocity
[tex]v_{x}=\dfrac{d}{t}[/tex]
Put the value into the formula
[tex]v_{x}=\dfrac{0.80}{0.545}[/tex]
[tex]v_{x}=1.46\ m/s[/tex]
(b). We need to calculate the final velocity
Using equation of motion
[tex]v_{f}^2=u^2+2as[/tex]
Put the value into the formula
[tex]v_{f}^2=0+2\times9.8\times1.46[/tex]
[tex]v_{f}=\sqrt{28.616}[/tex]
[tex]v_{f}=5.34\ m/s[/tex]
The velocity is 5.34 m/s downward.
We need to calculate the direction
Using formula of direction
[tex]\tan\theta=\dfrac{v_{y}}{v_{x}}[/tex]
[tex]\theta=\tan^{-1}(\dfrac{5.34}{1.46})[/tex]
[tex]\theta=74.7^{\circ}[/tex]
Hence, (a). The horizontal velocity is 1.46 m/s.
(b). The direction of the mug's velocity just before it hit the floor is 74.7° below the horizontal.
