Question

A worker kicks a flat object lying on a roof. The object slides up the incline 10.0 m to the apex of the roof, and flies off the roof as a projectile. What maximum height (in m) does the object attain? Assume air resistance is negligible, vi = 15.0 m/s, μk = 0.435, and that the roof makes an angle of θ = 43.5° with the horizontal. (Assume the worker is standing at y = 0 when the object is kicked.

Answer 1

Answer:15.20 m

Step-by-step explanation:

Given

initial velocity
`(v_i)=15 m/s`

inclined length=10 m

`\mu _k=0.435`

inclination
`\theta =43.5^(\circ)`

`F_(net)=f_r+mg\sin \theta`

`a_(net)=\mu _kg\cos \theta +g\sin \theta`

`a_(net)=0.435* 9.8* \cos 43.5+9.8* \sin 43.5`

`a_(net)=3.09+6.74=9.83 m/s^2`

`v^2-u^2=2as`

`v^2=15^2-2* (9.83)10`

`v=5.31 m/s`

So Particle launches with a speed of 5.31 m/s at an angle of \theta
`=43.5`

`h_(max)=(u^2\sin^2\theta )/(2g)`

`h_(max)=((5.31)^2\sin ^2(43.5))/(2* 9.81)`

`h_(max)=0.679`

Total height raised is
`0.679+(10)/(\sin 43.5) =15.20 m`