The formula ℎ = −5𝑡 2 + 𝑣0 𝑡 + 𝑐 shows the height (h) in meters of a projectile after t seconds.
h = height
t = time
𝑣0 = initial velocity
c = starting height.
A scientist records the motion of a dolphin as it jumps
from the water. The function
ℎ(𝑡) = −5𝑡 2 + 10𝑡 models the dolphin’s height in
meters above the water after t seconds.
1. What is the initial velocity?
2. Graph the function.
3. What is the dolphin’s maximum height above the
water?
4. How long is the dolphin out of the water?
x-scale = 0.5 (up to 5 seconds)
y-scale = 0.5 (up to 5 meters)
The formula ℎ = −16𝑡 2 + 𝑣0 𝑡 + 𝑐 shows the height (h) in feet of a projectile after t seconds.
h = height
t = time
𝑣0 = initial velocity
c = starting height.
The height in feet of a soccer ball x seconds after it is
kicked into the air is modeled by the function
𝑦 = 48𝑥 – 16𝑥 2
1. What is the initial velocity?
2. Graph the function.
3. Does the soccer ball ever reach a height of 50 ft?
Prove your answer.
4. How long is the soccer ball in the air?
x-scale = 0.5 (up to 5 seconds)
y-scale = 5 (up to 40 feet)
The formula ℎ = −16𝑡 2 + 𝑣0 𝑡 + 𝑐 shows the height (h) in meters of a projectile after t
seconds.
h = height
t = time
𝑣0 = initial velocity
c = starting height.
The height in feet of a golf ball that is hit from the ground
can be modeled by the function 𝑓(𝑥) = −16𝑥 2 + 96𝑥,
where x is the time in seconds after the ball is hit.
1. What is the initial velocity?
2. Find the ball’s maximum height and the time it takes
the ball to reach this height.
3. Then find how long the ball is in the air.
4. Make sure to include a graph.
x-scale = 0.5 (up to 6 seconds)
y-scale = 20 (up to 160 feet)
The formula ℎ = −16𝑡 2 + 𝑣0 𝑡 + 𝑐 shows the height (h) in feet of a projectile after t seconds.
h = height
t = time
𝑣0 = initial velocity
c = starting height.
A water bottle rocket is shot upward with an initial velocity of 𝑣0 = 45 ft/sec from the roof of
a school, which is at c, 50 feet above the ground.
1. Write the equation for this problem.
2. Graph the equation.
3. What is the approximate vertex of this parabola
and what does it mean?
4. How long was the rocket in the air?
5. Why didn’t the rocket pass through the point (0,0)?
x-scale = 0.5 (up to 4 seconds)
y-scale = 10 (up to 80 feet)
The formula ℎ = −16𝑡 2 + 𝑣0 𝑡 + 𝑐 shows the height (h) in feet of a projectile after t seconds.
h = height
t = time
𝑣0 = initial velocity
c = starting height.
The height in feet of a football that is kicked can be modeled
by the function 𝑓(𝑥) = −16𝑥 2 + 64𝑥, where x is the time in
seconds after it is kicked. Find the football’s maximum
height and the time it takes the football to reach this height.
1.
2.
3.
4.
What is the initial velocity?
How long is the football in the air?
How high does the football go?
Make sure to include a graph.
x-scale = 0.5 (up to 4 seconds)
y-scale = 5 (up to 70 feet)
The formula ℎ = −5𝑡 2 + 𝑣0 𝑡 + 𝑐 shows the height (h) in meters of a projectile after t seconds.
h = height
t = time
𝑣0 = initial velocity
c = starting height.
The height of a firework in meters can by approximated by
ℎ = −5𝑡 2 + 30𝑡, where h is the height in meters and t is
time in seconds.
1. Find the time it takes the firework to reach the ground
after it has been launched.
2. Make sure to include a graph.
3. How high did the firework reach?
4. What is the initial velocity?
x-scale = 0.5 (up to 6 seconds)
y-scale = 3 (up to 60 meters)
The formula ℎ = −16𝑡 2 + 𝑣0 𝑡 + 𝑐 shows the height (h) in feet of a projectile after t seconds.
h = height
t = time
𝑣0 = initial velocity
c = starting height.
Invaders are slinging rocks from a catapult to break down the door to the castle. The rock
leaves the catapult with an initial velocity of 80 feet per second. The height of the rock t
seconds after it is hit is given by ℎ = −16𝑡 2 + 80𝑡.
1. How long is the rock in the air?
2. What is the maximum height of the rock?
3. How long after the rock is launched
does it reach its maximum height?
4. What is the height of the rock after 3.5
seconds?
5. At what times is the rock 64 feet in the air?
Explain.
x-scale = 0.5 (up to 5 seconds)
y-scale = 10 (up to 100 feet)