Understanding Graphs
A baseball player hits a ball upward at a velocity of 30 feet per second from a height of 5 feet.
Sketch a graph of the height of the ball over time from the moment they hit it to the moment it hits the ground.
Graph sketch (at time zero, height should be 5 and should have some upward curve before hitting maximum and heading back down)
If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation:
h(t) = -16t2 + 128t
If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second How long will it take for the rocket to return to the ground?
1. What are you looking for to answer this equation?
2. What mathematically on the parabola are you looking for?
3. What equation(s)/Formula(s) will you use to find it? (name and formula)
1. Time to hit the ground/Time in the air
2. Positive zero (x-intercept)
3. Quadratic formula (-b +/- sqrt(b2-4ac))/2a
Maria's height while jumping on a trampoline can be given by the equation
h(t) = -16t2+18t+5
What is the maximum height that Maria will reach? (include units and write to 2 decimal places)
10.06 feet
A soccer goalie kicks a ball from the ground upward with a velocity of 10 meters per second.
Sketch a graph of the height of the soccer ball from the moment he kicks it until it hits the ground. Label key points on the graph, and indicate (h,t) values if problem provides them.
Graph should start at height of zero and go upward, then downward. No values other than 0,0, labeled
A rocket is launched from atop a 101 foot cliff with an initial velocity of 116 ft/s. What equation represents the height of the rocket at a given time t?
h(t) = -16t2+116t+101
You are trying to dunk a basketball. You need to jump 2.5 ft in the air to dunk the ball. The height that your feet are above the ground is given by the function
h(t) = -16t2 + 12t . What is the maximum height your feet will be above the ground?
1. What on the parabola are you looking for to answer this question?
2. What equation/formula(s) will you use to find it?
1. height at vertex
2. axis of symmetry (-b/2a) and
h(aos)= -16(aos)^2+12(aos)
While working on a roof Lex dropped a hammer. The hammers height can be represented by the equation
h(t) = -16t2+20
After how long will the hammer hit the ground? (include units and write to 2 decimal places)
1.12 seconds
Joanie drops an egg off a 3 foot counter while she is cooking.
Sketch a graph of the height of the egg from the moment it is dropped until the time it hits the ground.
Label key points on the graph, and indicate (h,t) where problem has provided the information.
graph should start at (0,3) and should head downwards in a parabola.
The height of the grappling hook thrown upward is given by the function h(t) = – 16t2 + 32t + 5. What is the initial height of the grappling hook (include units)?
5 feet
Heather lightly tossed her cap up at the end of graduation. The height of her cap at a given time can be represented by h(t)=-16t2+5t+5.
1. What is the maximum height of her cap?
-what are you looking for/what equation will you use
2. When will her cap hit the ground?
-what are you looking for/what equation will you use
1. height at vertex; find aos (-b/2a) the plug into equation for t
2. positive zero (x-intercept)
quadratic formula
The height of a baseball is represented by
h(t) = -16t2+48t +4
How high is the ball after 2 seconds? (include units)
36 feet
Sketch the graph to represent the situation below, make sure to include key points on the graph and label values if given
Jane tosses an egg upward from the top of a 7 foot ladder with a velocity of 5 feet/second. It drops just as Jack (who is 5 feet tall) walks by and cracks on his head.
Graph should start at (0,7) and goes upward, then should show stopping at height of 5)
A ship drops an anchor in the harbor and the height of the anchor at a given time until it hits the water is given by h(t) = -4.9t2+30.
1. What is the initial height of the anchor? (include units)
2. What is the initial upward velocity of the anchor? (include units)
1. 30 meters
2. 0 meters/second
Jackie, who is 5 feet tall, dropped a penny off of a bridge. The bridge is 10 feet above the level of the water.
1. Write the equation to represent the height of the penny at time t,
2. Find out when it will hit the water- what are you looking for? What equation will you use?
1. h(t) = -16t2+15
2. positive zero quadratic formula
A diver is standing on a platform 24 ft above the pool. He jumps from the platform with an initial upward velocity of 8 ft/s.
Use the formula h(t) = -16t2 + v0t + h0
How long will it take for him to hit the water?
h(t)=-16t2+8t+24
use quadratic formula
1.5 seconds
Look at the graph of the height of an object in feet vs. time in seconds at this link.
https://www.desmos.com/calculator/5qxfnp4rn1
Identify (as close a possible) make sure to include units!:
1. Starting height
2. Time to maximum height
3. Maximum Height
4. Time in the air
1. 3
2. about 1.25 seconds
3. about 9.2 feet
4. 2.5 seconds
During World War I, mortars were fired from trenches 3 feet down. The mortars had a velocity of 150 ft/s.
Write an equation to represent the height of the mortar at any given time.
h(t) = -16t2 + 150t -3
One of the games at a carnival involves trying to ring a bell with a ball by hitting a lever that propels the ball into the air. The height of the ball is modeled by the equations h(t) = -16t2 + 39t . If the bell is 25 ft above the ground, will it be hit by the ball.
1. What are you looking for to answer this question?
2. What mathematically on the parabola are you looking for?
3. What formula(s)/equation(s) will you need?
1. Maximum height (to compare)
2. Axis of symmetry and t (y) coordinate of the vertex
3. -b/2a then plug into equation and solve for t
A trebuchet launches a boulder from the ground at an initial velocity of 78 meters per second. How long in seconds will it take for the boulder to reach the same height on the way down as it was after 2 seconds?
14 seconds