Question

problem 3
the graph represents an object that is shot upwards from a tower and then falls to the ground. the independent variable is time in seconds and the dependent variable is the objects height above the ground in meters.
a. how tall is the tower from which the object was shot?
b. when did the object hit the ground?
c. estimate the greatest height the object reached and the time it took to reach that height. indicate this situation on the graph.

Explanation:

a. The tower height is the object's height at time \(t=0\) (before being shot up), which is the y-intercept of the graph.
b. The object hits the ground when its height is 0, corresponding to the x-intercept on the right side of the graph.
c. The greatest height is the y-value at the vertex (highest point) of the parabola, and the time is the corresponding x-value of that vertex.

Answer:

a. 10 meters
b. 6 seconds
c. Greatest height: 90 meters, Time to reach it: 2 seconds (the vertex of the graph is at the point (2, 90), which marks the highest point of the object's trajectory)