An arrow is shot upward from the ground with an initial velocity of 150 feet per second

initial-velocity

#1

An arrow is shot upward from the ground with an initial velocity of 150 feet per second. A)how long after the arrow is released does it reach max height? B) what is the height?

Answer:

v in the equation is the initial velocity - 150 feet/sand s the initial position which is zero because it is shot from the ground: h(t)=-15t^2+150t - The arrow will reach it’s maximum height when its velocity is zero (it changes direction). The velocity (v) is the first derivative of the position(h) -> v(t) = h’(t) = -30t+150. Now we set this to zero to find at what time is the velocity zero: -30t+150 =
0 -> t=150/30=5sec -> It reaches its maximum height after 5 seconds. and that height is
h(5) = 375 feet

A) 5 seconds
B) 375 feet