Question

In: Physics

A grappling hook is fired from a cannon at ground level with an initial speed of...

A grappling hook is fired from a cannon at ground level with an initial speed of 40 m/s at an angle of 50 degree above the ground. It is a fired at a vertical cliff. The cliff is very high and we are very close. So we are sure that the hook will hit the face of the cliff.

Determine the x component of the initial velocity, and how that the y-component of the initial velocity is 30.6 m/s up.

It takes 4.0 second for the hook to hit the well. Determine the height of the hook at the point it hits the well and the y-component of the velocity at the time of impact.

Draw a graph of the y-component of the velocity vy as a function of the time for those 4.0 second the axes should be labeled, include units, and be to an appropriate scale.

Expert Solution

Vix = initial velocity in X-direction, Viy = initial velocity in Y-direction

Vi = initial velocity of hook = 40 m/s

in the triangle ABC, AC = adjacent = Vix , BC = opposite = Viy , AB = hypoteneuse = Vi

using trigonometric ratio , sin50 = BC/AB = Viy / Vi so Viy = Vi sin50

Viy = 40 x sin50 ( since Vi = 40 m/s)

Viy = 40 x (0.766) = 30.64 m/s

similarly using , cos 50 = AC/AB = Vix/Vi

Vix = Vi cos50

Vix = 40 cos50 (since Vi = 40 m/s)

Vix = 40 (0.643) = 25.71 m/s

to calculate the height which is in Y-direction , we need to use kinematics equation

considering the motion of hook from A to P along Y-direction. we list the data as

V_iy = 30.64 m/s , a_y = -9.8 m/s² (acceleration due to gravity) , t = 4 sec , Y_o =0 m ,Y = ''h'' (height)

so using the kinematics equation , Y = Y_o + V_iy t + (0.5) a_y t²

h = 0 + (30.64 m/s)(4 sec) + (0.5) (-9.8 m/s² ) (4 sec)²

h = 44.16 m

calculating Y-component of velocity at time of impact :-

considering the motion of hook from A to P along Y-direction. we list the data as

V_iy = 30.64 m/s , a_y = -9.8 m/s² (acceleration due to gravity) , t = 4 sec , V_fy = ?

using the kinematics equation :- V_fy = V_iy + at = 30.64 m/s + (-9.8 m/s² ) (4 sec)

V_fy = -8.56 m/s

graph :-

genius_generous answered 1 week ago

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