SOLUTION: I am stuck on this problem. Jacob is standing at the edge of a 3000 foot deep canyon. He kicks a ball into the air with a initial upward velocity of 32 feet per second. when will

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The general form of the equation for the height of an object propelled upward with an initial velocity of v from an initial height of h is , and since the depth of the canyon by which Jacob is standing is really irrelevant, your initial equation is correct. The initial height is zero feet.

Now you would like to find out at what time (t) will the ball return to its initial height of 0 ft.
Setting h(t) = 0 ft. you can write:
Solve for t by factoring -16t from both sides.
Apply the zero product principle.
Add 2 to both sides.

The ball will return to its initial height of 0 ft. in 2 seconds.
Check: Set t = 2
Solve for h.

ft.