# 1-D Motion Kinematics Problem

## Homework Statement

A missile is launched into the air at an initial velocity of 80 m/s. It is moving with constant velocity until it reaches 1000m, when the engine fails.
a) How long does it take it to reach 1000m
b)How high the missile go?
c)How long does it take for it to fall back to the earth?
d)How long does it stay in the air?
e)How fast is it going when it hits the ground?

## Homework Equations

the 5 kinematic equations: d=v1t + 0.5at^2, d=v2t + 0.5at^2, v2^2=v1^2 + 2ad,
d=(v1+v2)/2 all x t

## The Attempt at a Solution

Ok so i'm confused as to whether the missile instantly starts falling after 1000 m or if it continues for a bit then starts falling. For a) assuming it keeps going up after the engine fails I got t=12.5s but assuming the max height is 1000m I got t=30s

For b) again i'm confused as to whether the max height is 1000m or not and I can't really do the rest without clearing this confusion up

## The Attempt at a Solution

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rude man
Homework Helper
Gold Member
Why would it suddenly stop after reaching 1000m? It's still going at 80m/s at that altitude.

The motion here is split in three parts.
1st: uniform rectilinear motion with speed 80m/s until it is 1000 m high
2nd: uniformly decelerated motion with initial velocity and acceleration given by -g (remember that it is still going up, so the terrestrial gravity is opposed to the motion)
3rd: uniformly accelerated motion when falling until reaches the ground (acceleration again g but this time in the direction of the motion as the missile is falling).

What you have to do is compute the time the first phase takes, then with the usual two equations for accelerated motion (data are initial velocity 80 m/s, initial height 1000 m, final velocity 0 m/s) you can compute the final height and the time to reach it, then you can compute the time it takes from this final height to reach the ground and how fast it goes when touching ground (data are this time initial height you just computed, initial velocity 0 m/s, final height 0 m).

Ok thanks, that clears things up