Will give fan and medal. How long would the rocket take to fall back to Earth? A model rocket is launched from the ground with an initial velocity of 160 ft/sec. How long will it take the rocket to reach its maximum height? Show all work in the space provided.

I worked up the equation myself

Height = f(t)
= 160t – 16t²
f(1) = 144 ft.

Velocity = f`(t)
= 160 – 32t
f`(1) = 128 ft/s.

f`(t) = 0 at the maximum height
0 = 160 – 32t
32t = 160
t = 5
5 seconds

f(t) = 160t – 16t²
f(5) = 160(5) – 16(5)²
f(5) = 800

Question

Will give fan and medal. How long would the rocket take to fall back to Earth? A model rocket is launched from the ground with an initial velocity of 160 ft/sec. How long will it take the rocket to reach its maximum height? Show all work in the space provided.

I worked up the equation myself

Height = f(t)
       = 160t – 16t²
       f(1) = 144 ft.

Velocity = f`(t)
       = 160 – 32t
       f`(1) = 128 ft/s.

f`(t) = 0 at the maximum height
       0 = 160 – 32t
       32t = 160
       t = 5
       5 seconds

f(t) = 160t – 16t²
       f(5) = 160(5) – 16(5)²
       f(5) = 800

anonymous · Answer

So with this equation done, how long would it take for the rocket to fall back to earth from the time it was launched if it's Parachute failed to deploy?

anonymous · Answer

@phi can you help me?

welshfella · Answer

you can use one of the equations of motion for constant acceleration. In this case the acceleration is due to gravity and = 32 ft /s^2

v = u + at

at maximum height v = final velocity = 0 , u = 160 and a = -32 ( as the acceleration acts in opposite direction to motion)

0 = 160 - 32t
t = 160/32 secnds

welshfella · Answer

t = 5 seconds as you said

anonymous · Answer

@welshfella can I ask another question?