Two stones are thrown simultaneously, one straight upward fromthe base of a clif
ID: 1751939 • Letter: T
Question
Two stones are thrown simultaneously, one straight upward fromthe base of a cliff and the other straight downward from the top ofthe cliff. The height of the cliff is 5.84 m. The stones are thrownwith the same speed of 8.48 m/s. Find the location (above the baseof the cliff) of the point where the stones cross paths.D = Two stones are thrown simultaneously, one straight upward fromthe base of a cliff and the other straight downward from the top ofthe cliff. The height of the cliff is 5.84 m. The stones are thrownwith the same speed of 8.48 m/s. Find the location (above the baseof the cliff) of the point where the stones cross paths.
D =
Explanation / Answer
The velocity of the stone thrown up is given by: vup = 8.48 - g.t and the velocity of the stone thrown down is given by: vdn = 8.48 + g.t The average velocity is (the initial velocity + the finalvelocity)/2 So average velocity for vup = (8.48 + (8.48 - g.t))/2 =4.24 + 4.24 - g.t/2 = 8.48 - g.t/2 and the average velocity for vdn =(8.48 + 8.48 + g.t)/2= 8.48 + gt/2 The distance fallen by the dropped stone is given by thetime*average velocity, = t(8.48 + gt/2) = 8.48t +gt2/2 The distance covered by the thrown up stone is then: 8.48t -gt2/2 At the point where they cross, the distance covered is the same,so: 8.48t + gt2/2 = 5.84 - (8.48t -gt2/2) (the thrown UP stone starts at 0 m altitude but the thrown DOWNstone starts at + 5.84m) Solve the equation: 8.48t + 8.48t + gt2/2 -gt2/2 = 5.84 and 16.96t = 5.84 Therefore t = 5.84/16.96 = 0.34 s We're asked to find how high off the ground this is. Simply put tinto the formula: vup = 8.48 - g.t and we get vup = (8.48 -0.34*9.8) = 5.15 m/s Since the initial velocity = 8.48 and the final velocity = 5.15then the average velocity = 6.81 m/s And t = 0.34 So using d = v.t we get d = 6.81 * 0.34 = 2.31 m which is thedistance above the ground where the paths cross. I have worked through this using the fundamental laws so as to showyou how the system works, rather than using s = 1/2 gt2
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