Construct a graph corresponding to the stone's vertical displacement, y(t).?

Question

A stone is thrown upward from the edge of a cliff, reaches its maximum height, and then falls down into the valley below. A motion diagram for this situation is given(Figure 1) , beginning the instant the stone leaves the thrower’s hand. Construct the corresponding motion graphs taking the acceleration due to gravity as exactly 10 m/(s^2) . Ignore air resistance. In all three motion graphs, the unit of time is in seconds and the unit of displacement is in meters. In plotting the points, round-off the coordinate values to the nearest integer.

Here is the figure and solution: http://i.imgur.com/YLhrpb4.png

The solution does not say what the coordinates are at each point so I'm REALLY REALLY REALLY confused how the **** they got that answer. Can someone please help me?!

Here is the figure and solution: http://i.imgur.com/YLhrpb4.png

The solution does not say what the coordinates are at each point so I'm REALLY REALLY REALLY confused how the **** they got that answer. Can someone please help me?!

Whome · Accepted Answer

Knowing that gravity is 10 m/s² allows one to add in the vertical position points on the graphs using kinematic equations.

at 2 seconds, the velocity (slope of the position curve) is zero so the initial velocity must have been.

v₀ = at
v₀ = (10)2
v₀ = 20 m/s

then using the equation

y = v₀t + ½gt²

y = 20t + ½(-10)t²

y(t) = 20t - 5t²

y(0) = 0 m
y(1) = 15 m
y(2) = 20 m
y(3) = 15 m
y(4) = 0 m
y(5) = -25 m
y(6) = - 60 m

Anonymous · Answer

the graph doesn't go down to -60

Daniela · Answer

Thank you so much!! Your answer was very helpful

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Construct a graph corresponding to the stone's vertical displacement, y(t).?

3 Answers