Algebra II Pre AP



Algebra II Pre AP Name _____________________________

Notes & Worksheet – Quadratic Function Applications III

Projectile Motion

[pic] (feet) [pic] (meters)

Steps for solving motion problems.

Step 1: Write an equation of the height as a function of time by substituting the velocity and initial height in

the correct formula.

Step 2: Sketch a graph and label. Use the calculator and adjust the window to find the intercepts and vertex.

Step 3: Answer the questions.

Examples

1) An object is propelled vertically upward from the ground with an initial velocity of 20 meters per second.

a) When will the object be 15 meters above the ground?

b) When will it strike the ground?

c) Will the object reach a height of 100 meters?

d) What is the maximum height?

2) A ball is thrown vertically upward from the top of a building 96 ft tall with an initial velocity of 80 ft/s.

a) After how many seconds does the ball strike the ground?

b) After how many seconds will the ball pass the top of the building on its way down?

c) What is a reasonable domain and range.

3) When a ball was thrown vertically upward, it was released four feet above the ground with an initial velocity of 75

feet per second. When is the ball less than 30 feet above the ground?

For each problem:

1) Write the quadratic equation for the height as a function of time unless equation is given.

2) Sketch a graph. Label the intercepts, vertex and axes. Write the window you used.

3) Answer the questions.

1. A projectile is launched upward from ground level with an initial speed of 98 m/s.

a. When will it return to the ground?

b. How high will it go?

2. A signal flare is fired upward form ground level with an initial speed of 285 m/s. A balloonist cruising at a height of 2450 meters sees it pass on the way up. How long will it be before the flare passes the balloonist again on the way down?

3. Luis wanted to throw an apple to Kim, who was on a balcony 40 feet above him, so he tossed it upward with an initial speed of 52 ft/s. Kim missed it on the way up, but then caught it on the way down. How long was the apple in the air?

4. A ball is thrown upward from the top of a 98 meter tower with an initial speed of 39.2 m/s. When is the ball 120 m above the ground? When will it hit the ground?

5. A ball is kicked upward from ground level with an initial speed of 86 ft/s. How high will it go?

6. A ball is thrown directly upward from ground level with an initial speed of 50 ft/s.

a. When is the ball less than 20 feet above the ground?

b. How high will it go?

c. When will it hit the ground?

7. A rocket is moving vertically upward with speed 245 m/s when its fuel runs out. How much farther will it travel upward before starting to fall back to the ground?

8. The distance [pic], in feet, required for a vehicle traveling at [pic] mi/h to come to a stop is given approximately by [pic]. If an automobile in a 55 mi/h speed zone required 240 ft to stop, was its speed within the legal limit?

9. The path of a soccer ball kicked from the ground can be modeled by the equation [pic], where [pic] is the horizontal distance (in feet) from where the ball was kicked and [pic] is the corresponding height (in feet).

a. A soccer goal is 8 feet high. Write and solve an inequality to determine at what distances from where the ball was kicked will the ball be low enough to go into the goal.

b. A soccer player kicks the ball toward the goal from a distance of 15 feet away. No one is blocking the goal. Will the player score a goal?

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