Question

The function H(t) = -16t2 + vt + s shows the height H (t), in feet, of a projectile launched vertically from s feet above the ground after t seconds. The initial speed of the projectile is v feet per second.

Part A: The projectile was launched from a height of 82 feet with an initial velocity of 60 feet per second. Create an equation to find the time taken by the projectile to fall on the ground. (2 points)

Part B: What is the maximum height that the projectile will reach? Show your work. (2 points)

Answer 1

Part C: Another object moves in the air along the path of g(t) = 10 + 63.8t where g(t) is the height, in feet, of the object from the ground at time t seconds.

Use a table to find the approximate solution to the equation H(t) = g(t), and explain what the solution represents in the context of the problem? [Use the function H(t) obtained in Part A, and estimate using integer values] (4 points)

Part D: Do H(t) and g(t) intersect when the projectile is going up or down, and how do you know? (2 points)

Answer 2

@triciaal

Answer 3

part A
using the function H(t)
s = 82 , v = 60 H(t) = 0 find t
you will have a quadratic 2 values for t one value will be 0

Answer 4

sorry part A just the equation
Part B solve the equation

Answer 5

Part B the time/2 for the maximum height reached

Answer 6

how would i set up the equation for part a

Answer 7

part C
Use a table to find the approximate solution to the equation H(t) = g(t)
for any value of t find the value of Ht) and the value g(t)
when H(t) = g(t) this is the time they will meet

Answer 8

part a you are just substituting the given values v = 60 s = 82 etc

Answer 9

part A is to write the equation

Answer 10

so it would look like this H(t) = -16t2 + 60t + 82

Answer 11

yes

Answer 12

ok can you help me with part b also cause im bad at solving these

Answer 13

for part A equation = 0 the ground has a height of 0 H(t) = 0

Answer 14

so its 0 = -16t2 + 60t + 82

Answer 15

yes then solve to find t start (t = 0) and after how long will be back on ground (t= value when solved)

Answer 16

ok wait i thought part b where we needed to solve it

Answer 17

@triciaal

Answer 18

yes Part A write the equation
Part B solve the equation this will give you t find t/2 use this value to find the maximum height

Answer 19

ok can you help me with part b

Answer 20

you need to give me time to read, interpret and do as well as answer any questions you have in-between

Answer 21

mkay im sorry for rushing

Answer 22

now i forgot where i was

Answer 23

let's solve the quadratic.
you can divide everything by 4 to work with smaller numbers
what is -16 t^2 + 60 t + 82 = 0 divided by 4?

Answer 24

-4t^2 + 15t + 20.5

Answer 25

you are correct I thought it was 84

Answer 26

let's use the formula to solve
a = -4 b = 15 c = 20.5