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A block is projected up a frictionless inclined plane with initial speed v0 = 1.72 m/s. The angle of incline is θ = 44.8°. (a) How far up the plane does it go? (b) How long does it take to get there? (c) What is its speed when it gets back to the bottom?

Respuesta :

Explanation:

Given

initial velocity(v_0)=1.72 m/s

[tex]\theta =44.8{\circ}[/tex]

using [tex]v^2-u^2=2as[/tex]

Where v=final velocity (Here v=0)

u=initial velocity(1.72 m/s)

a=acceleration   [tex](gsin\theta )[/tex]

s=distance traveled

[tex]0-(1.72)^2=2(-9.81\times sin(44.8))s[/tex]

s=0.214 m

(b)time taken to travel 0.214 m

v=u+at

[tex]0=1.72-gsin(44.8)\times t[/tex]

[tex]t=\frac{1.72}{9.8\times sin(44.8)}[/tex]

t=0.249 s

(c)Speed of the block at bottom

[tex]v^2-u^2=2as[/tex]

Here u=0 as it started coming downward

[tex]v^2=2\times gsin(44.8)\times 0.214[/tex]

[tex]v=\sqrt{2.985}[/tex]

v=1.72 m/s