A student stands at the edge of a cliff and throws a stone horizontally over the

Question

A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v(i) = 18.0 m/s. The cliff is h = 50.0 m above a body of water. a.) What are the coordinates of the initial position of the stone? b.) What are the components of the initial velocity of the stone? c.) What is the appropriate analysis model for the vertical motion of the stone? d.) What is the appropriate analysis model for the horizontal motion of the stone? e.) Write symbolic equations for the x and y components of the velocity of the stone as a function of time. f.) Write symbolic equations for the position of the stone as a function of time. g.) How long after being released does the stone strike the water below? h.) With what speed and angle of impact does the stone land?

Explanation / Answer

a) Initial coordinates =(0,0) in meters b) Initial velocity: vx= 18m/s vy =0 so, v= (18)i + 0j c)Vertical motion: particle under constant acceleration. d) Horizontal motion: particle under no force. e)vx(t) = 18 + (ax)*t and ax=0 so, vx(tt) =18m/s f)vy(t) =0 + (ay)*t and ay =-g=-9.8m/s2 so, vy(t) =-gt g)sy(t) = displacement along y at time t then: s(y) =0 + (1/2)*(-g)*(t^2) = -(g/2)t^2 =-50m at time of collision so, t=Sqrt(100/g) =3.194s h) find v(t) at t=3.194s so, vx =18m/s and vy= -9.8*3.194 =-31.311 m/s so speed = 36.11m/s and angle = 60.16 degrees

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