A rock is kicked horizontally at 15 m/s from a hil...

Question

A rock is kicked horizontally at 15 m/s from a hill with a 45 degree slope (figure below). How long does it take for the rock to hit the ground?

Patrick Ford · Accepted Answer

In this problem, we'll consider the equation below to relate the displacement of the rock and time period in the horizontal direction.x=x0+v0t[readmore]where x0 is the initial displacement, v0 is the initial velocity of the rock, and t is the time taken by the rock to reach the ground. Since the initial displacement of the rock is zero, our displacement equation will be:x=v0tSolving for t, we have:t=xv0Displacement of the rock and the time period in the vertical direction is related by the equation:y=y0+vy0t+12ayt2, where y0 is the initial vertical displacement of the rock, vy0 is the initial vertical velocity of the rock, and ay is the acceleration due to gravity.y0 = 0 mvy0 = 0 m/sWe already have t = x/v0Substituting, we'll have:y=0+(0)(xv0)+12(-g)(xv0)2=-12g(xv0)2 Now, let's consider the point of launch as the origin of the coordinate and the final point to be (x,y).The slope of the projectile will be:∆y∆x=tanθy-0x-0=tan(360°-45°)yx=-1x=-y This implies that the vertical component of the displacement is equal to the horizontal component of the displacement. That is, x = -y.Now we'll have:x=-[-12g(xv0)2]x=12gx2v0x=2v02gSubstituting to the equation for t, t = x/v0, gives:t=2v02gv0=2v0g=(2)(15)9.81t = 3.06 s.The time it takes the rock to hit the ground is 3.06 s.

Problem: A rock is kicked horizontally at 15 m/s from a hill with a 45 degree slope (figure below). How long does it take for the rock to hit the ground?

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Problem Details

Problem: A rock is kicked horizontally at 15 m/s from a hill with a 45 degree slope (figure below). How long does it take for the rock to hit the ground?

FREE Expert Solution

Problem Details

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