SAT
Explain a height at one moment in the flight.
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Time, then height
A tennis ball is tossed upward.
h(t) is the height of the tennis ball, in feet, t seconds after it leaves the hand.
h(t) = −16t² + 56t + 4
h(1) = 44
The tennis ball is 44 feet above the ground 1 second after it leaves the hand.
Letters from the situation
h stands for the height, in feet.
t stands for the time, in seconds.
Read h(1) = 44 as the time first, then the height.
Work these three in a session.
A soccer ball is thrown upward.
h(t) is the height of the soccer ball, in feet, t seconds after it is thrown.
h(t) = −16t² + 72t + 8
h(3) = 80
Which choice best explains this statement in the situation?
t = 3
h(3) = 80
The number inside the parentheses is the time, in seconds.
The number after the equals sign is the height, in feet, at that time.
The soccer ball is 80 feet above the ground 3 seconds after it is thrown.
The equation does not need to be solved.
3 feet after 80 seconds swaps the time and the height.
Answer: B. The soccer ball is 80 feet above the ground 3 seconds after it is thrown.
A model rocket is launched upward.
a(t) is the altitude of the rocket, in meters, t seconds after it is launched.
a(t) = −5t² + 40t + 10
a(2) = 70
Which choice best explains this statement in the situation?
t = 2
a(2) = 70
The number inside the parentheses is the time, in seconds.
The number after the equals sign is the altitude, in meters, at that time.
The rocket is 70 meters above the ground 2 seconds after it is launched.
The equation does not need to be solved.
2 meters after 70 seconds swaps the time and the altitude.
Answer: D. The rocket is 70 meters above the ground 2 seconds after it is launched.
A football is punted upward.
h(t) is the height of the football, in feet, t seconds after it is punted.
h(t) = −16t² + 64t + 12
h(1) = 60
Which choice best explains this statement in the situation?
t = 1
h(1) = 60
The number inside the parentheses is the time, in seconds.
The number after the equals sign is the height, in feet, at that time.
The football is 60 feet above the ground 1 second after it is punted.
The equation does not need to be solved.
1 foot after 60 seconds swaps the time and the height.
Answer: A. The football is 60 feet above the ground 1 second after it is punted.
Try these five on your own.
A baseball is thrown upward.
h(t) is the height of the baseball, in feet, t seconds after it is thrown.
h(t) = −16t² + 80t + 6
h(4) = 70
Which choice best explains this statement in the situation?
t = 4
h(4) = 70
The number inside the parentheses is the time, in seconds.
The number after the equals sign is the height, in feet, at that time.
The baseball is 70 feet above the ground 4 seconds after it is thrown.
The equation does not need to be solved.
4 feet after 70 seconds swaps the time and the height.
Answer: C. The baseball is 70 feet above the ground 4 seconds after it is thrown.
A golf ball is hit upward.
h(t) is the height of the golf ball, in feet, t seconds after it is hit.
h(t) = −16t² + 88t + 4
h(4) = 100
Which choice best explains this statement in the situation?
t = 4
h(4) = 100
The number inside the parentheses is the time, in seconds.
The number after the equals sign is the height, in feet, at that time.
The golf ball is 100 feet above the ground 4 seconds after it is hit.
The equation does not need to be solved.
4 feet after 100 seconds swaps the time and the height.
Answer: B. The golf ball is 100 feet above the ground 4 seconds after it is hit.
A firework is fired upward.
a(t) is the altitude of the firework, in meters, t seconds after it is fired.
a(t) = −5t² + 45t + 10
a(7) = 80
Which choice best explains this statement in the situation?
t = 7
a(7) = 80
The number inside the parentheses is the time, in seconds.
The number after the equals sign is the altitude, in meters, at that time.
The firework is 80 meters above the ground 7 seconds after it is fired.
The equation does not need to be solved.
7 meters after 80 seconds swaps the time and the altitude.
Answer: A. The firework is 80 meters above the ground 7 seconds after it is fired.
An arrow is shot upward.
h(t) is the height of the arrow, in feet, t seconds after it is shot.
h(t) = −16t² + 96t + 8
h(5) = 88
Which choice best explains this statement in the situation?
t = 5
h(5) = 88
The number inside the parentheses is the time, in seconds.
The number after the equals sign is the height, in feet, at that time.
The arrow is 88 feet above the ground 5 seconds after it is shot.
The equation does not need to be solved.
5 feet after 88 seconds swaps the time and the height.
Answer: D. The arrow is 88 feet above the ground 5 seconds after it is shot.
A water balloon is tossed upward.
h(t) is the height of the water balloon, in feet, t seconds after it is tossed.
h(t) = −16t² + 64t + 2
h(3) = 50
Which choice best explains this statement in the situation?
t = 3
h(3) = 50
The number inside the parentheses is the time, in seconds.
The number after the equals sign is the height, in feet, at that time.
The water balloon is 50 feet above the ground 3 seconds after it is tossed.
The equation does not need to be solved.
3 feet after 50 seconds swaps the time and the height.
Answer: C. The water balloon is 50 feet above the ground 3 seconds after it is tossed.
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