an arrow starts at a height of 20m at a 30 degree angle with an initial velocity of 62m/sec. Write and sketch a function to represent the height of the arrow after t seconds.

Question

This problem has 3 parts. I want to learn how it's done I just don't understand it and need help bad.

Answer 1

(A)

The equation for the height as a function of time is

h(t) = -gt²/2 + v₀sinθ t + h₀

g = acceleration of gravity = 9.8 m/s²

v₀ = initial speed = 62 m/s

θ = launch angle above the horizontal = 30°

h₀ = initial height = 20 m

In meters,

h(t) = -4.9t² + 62sin30° t + 20

(B)

To find time when arrow reaches 60 m, set h(t) = 60 and solve for t.

-4.9t² + 62sin30° t + 20 = 60

-4.9t² + 62sin30° t - 40 = 0

Solve this last equation for t using the quadratic formula. You will get 2 positive solutions. The lower solution is the time to reach 60 on the way up. The higher solution is the time to reach 60 on the way down.