How Do You Solve a 1-D Motion Kinematics Problem Involving a Missile?

[dazed6531]

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

 

[rude man]

Why would it suddenly stop after reaching 1000m? It's still going at 80m/s at that altitude.

 

[tia89]

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).

 

[dazed6531]

Ok thanks, that clears things up

 

[Nickie]

.

I would approach this problem by first clarifying the initial conditions and assumptions. It is important to know if the missile is launched at an angle or vertically, and if it continues to move at a constant velocity after the engine fails. This information will help in determining the correct equations to use and the appropriate values for the variables.

Assuming that the missile is launched vertically and continues to move at a constant velocity after the engine fails, the answers to the questions are as follows:

a) To reach 1000m, the missile will take t = 1000m/80m/s = 12.5s.

b) The missile will reach its maximum height at t = 12.5s, and the maximum height can be calculated using the equation d = v1t + 0.5at^2. Since the velocity is constant and there is no acceleration, the maximum height will be 1000m.

c) The missile will start falling back to Earth immediately after reaching its maximum height. The time it takes to fall back to Earth can be calculated using the equation d = v1t + 0.5at^2, where d = 1000m (maximum height), v1 = 0m/s (velocity at the top of the trajectory), and a = -9.8m/s^2 (acceleration due to gravity). Solving for t, we get t = 14.3s.

d) The missile stays in the air for a total of t = 12.5s + 14.3s = 26.8s.

e) When the missile hits the ground, its velocity can be calculated using the equation v2^2 = v1^2 + 2ad, where v2 = 0m/s (velocity at the ground), v1 = 80m/s (initial velocity), a = -9.8m/s^2 (acceleration due to gravity), and d = 1000m (maximum height). Solving for v2, we get v2 = 126.5m/s. This is the velocity at which the missile hits the ground.