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In an experiment two identical rocks are simultaneously thrown from the edge of a cliff a distance to above the ground. Rock A is thrown vertically upward with speed vo and rock B is thrown vertically downward with speed vo. Rock A and rock B strike the ground at times, and f, respectively. Consider the positive vertical direction to be upward. (a) On the axes given below, sketch and label graphs of the velocity as a function of time for rock A and rock Label the time fg. Times A and are given on the graph. Velocity Time (b) Rock B hits the ground at time fg. Derive an equation for the time it takes rock A to hit the ground in terms of vo. lg. and physical constants, as appropriate.
In an experiment two identical rocks are simultaneously thrown from the edge of a cliff a distance to above the ground. Rock A is thrown vertically upward with speed vo and rock B is thrown vertically downward with speed vo. Rock A and rock B strike the ground at times, and f, respectively. Consider the positive vertical direction to be upward. (a) On the axes given below, sketch and label graphs of the velocity as a function of time for rock A and rock Label the time fg. Times A and are given on the graph. Velocity Time (b) Rock B hits the ground at time fg. Derive an equation for the time it takes rock A to hit the ground in terms of vo. lg. and physical constants, as appropriate.
Final answer:In the described physics question, the time it takes for Rock A to hit the ground, after being thrown upwards off a cliff, can be derived using the equation of motion: t = √[(2h) / g], where h is height of the cliff and g is acceleration due to gravity. The speed of initial throw doesn't affect this time.Explanation:Theexperimentdescribed in the question involves two identical rocks being thrown off a cliff with the same speed but in opposite directions: upwards for Rock A and downwards for Rock B. The descent time for each rock is further given and it's asked to derive the time it takes for Rock A to hit the ground.Firstly, the velocity of each rock as afunctionof time can be represented by the equation v = vo + gt where v is the final velocity, vo is the initial velocity, g is acceleration due to gravity, and t is time. Since we're considering the upward direction as positive, the gravity will be negative. Therefore, for Rock A thrown upwards, we would have: v = vo - gt and for Rock B thrown downwards, it would be: v = -vo - gt.To derive the time it takes for Rock A to hit the ground in terms of vo, lg, and physical constants, use the equations ofmotion. In this case, the most applicable equation would be the one that interrelates displacement (d), initial velocity (vo), time (t) and acceleration (a): d = vot + 0.5at². Given that we're starting from a cliff, the displacement (d) will be the cliff's height (h). Therefore, rearranging terms to find time would result in: t = √[(2h) / g].Notice that the time it takes for Rock A to hit the ground is dependent on the height of the cliff and the acceleration due to gravity and independent of the initial speed with which the rock was thrown.Learn more about Equations of Motion here:brainly.com/question/35709307#SPJ12...