1. A trebuchet launches a pumpkin on a parabolic arc from a height of 47 ft at a velocity of 40 ft/s which gives the
following function equation h(t)= -16t^2 + 40t + 47. State the vocabulary term that is being described by the
following questions. Do not solve for any of the key features. questions a b c and d
a. When will the pumpkin reach the ground?
The pumpkin will reach the ground at
b. What is the maximum height the pumpkin reaches?
C. When does the pumpkin reach its maximum height?
d. What is the starting height of the pumpkin?

a) 3.37 seconds

b) 75.85 feet

c) 1.25 seconds

d) 47 feet

Step-by-step explanation:

a) I could use kinematic equations here, but I'll use the one provided. Height as a function of time equals 0 when the pumpkin reaches the ground, so 0=(-16t^2)+40t+47 is your equation here. Solve for t. t=3.37

b) If you have a graphing calculator, just use maximum feature. If not, use the formula x=-b/2a. x=-40/-32, x=1.25.

Now, plug 1.25 in as t, and you'll get y=75.85ft

c) alreaady found in previous part

d) this is the constant in the formula, or the y-intercept, which is 47 (because there's no variable attached).

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.