Vertical Motion Problem Solving



Vertical Motion Problem Solving Name _______________________

Date _________ Period __________

1. A startled armadillo jumps straight into the air with an initial vertical velocity of 14 feet per second. After how many seconds does it land on the ground?

2. A spittlebug jumps into the air with an initial vertical velocity of 10 feet per second. Write an equation that gives the height of the spittlebug as a function of the time (in seconds) since it left the ground. The spittlebug reaches its maximum height after 0.3125 second. How high can it jump?

3. One football is kicked into the air with an initial vertical velocity of 44 feet per second. Another football is kicked into the air with an initial vertical velocity of 40 feet per second. Which football is in the air for more time? Justify your answer.

4. An athlete throws a discus from an initial height of 6 feet and with an initial vertical velocity of 46 feet per second. Write an equation that gives the height of the discus as a function of the time since it left the athletes hand. After how many seconds does the discus hit the ground?

5. A diver dives from a cliff when her center of gravity is 46 feet above the surface of the water. Her initial vertical velocity leaving the cliff is 9 feet per second. After how many seconds does her center of gravity enter the water?

6. While standing on a ladder, you drop a paintbrush from a height of 25 feet. After how many seconds does the paintbrush land on the ground?

7. An arch of balloons decorates the stage at a high school graduation. The balloons are tied to a frame. The shape of the frame can be modeled by the graph of the equation y = [pic] where x and y are measured in feet. Make a table of values that shows the height of the balloon arch for x = 0, 2, 5, 8, and 11 feet. For what additional values of x does the equation make sense? Explain. At approximately what distance from the left end does the arch reach a height of 9 feet?

8. A ball is thrown up into the air from a height of 5 feet with an initial vertical velocity of 56 feet per second. How many times does the ball reach a height of 54 feet? Explain your answer.

9. The path of a jumping robot can be modeled by the graph of the equation y = -10x2 + 30x where x and y are both measured in feet. On a coordinate plane, the ground is represented by the x-axis, and the robot’s starting position is the origin. The robot’s maximum height is 22.5 feet. What is the robot’s horizontal distance from its starting point when its height is 22.5 feet? How far has the robot traveled horizontally when it lands on the ground? Explain your answer.

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