Answer:
A
Step-by-step explanation:
The equation of a line passing through the origin is
y = mx ( m is the slope )
To find m use the slope formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (1, 1) and (x₂, y₂ ) = (- 1, - 1) ← 2 points on the line
m = =
= 1
y = x ← is the equation of the line → A
All of these equations will be set up as: h(t) = +v₀t + h₀ where g represents gravity, v₀ represents initial velocity, and h₀ represents initial height. When working with ft/sec, g = 32. So, -g/2 = -16
1a) Length of time to reach its maximum height means you are looking for the x-value of the vertex (aka Axis Of Symmetry).
h(t) = -16t² + 160t
AOS: x = =
= 5
Answer: 5 sec
1b) Length of time to fall to the ground means you are looking for the x-intercept when height (y-value) = 0.
h(t) = -16t² + 160t
0 = -16t² + 160t
0 = -16t(t - 10)
0 = -16t 0 = t - 10
t = 0 t = 10
t = 0 is when it started, t = 10 is when fell to the ground.
Answer: 10 sec
2c) Same concept as 1a
h(t) = -16t² + 288t
AOS: x = =
= 9
Answer: 9 sec
2d) Same concept as 1b
h(t) = -16t² + 288t
0 = -16t² + 288t
0 = -16t(t - 18)
0 = -16t 0 = t - 18
t = 0 t = 18
Answer: 18 sec
3e) Same concept as 1a
h(t) = -16t² + 352t
AOS: x = =
= 11
Answer: 11 sec
3f) Same concept as 1b
h(t) = -16t² + 352t
0 = -16t² + 352t
0 = -16t(t - 22)
0 = -16t 0 = t - 22
t = 0 t = 22
Answer: 22 sec
