A rocket is sent to shoot down an invading spacecraft that is hovering at an altitude of $ 1500 \, \text{m} $. The rocket is launched with an initial velocity of $ 180 \, \text{m/s} $. Find the following:

Question

A rocket is sent to shoot down an invading spacecraft that is hovering at an altitude of $ 1500 \, \text{m} $. The rocket is launched with an initial velocity of $ 180 \, \text{m/s} $. Find the following:(a) The minimum velocity needed to hit the spaceship.
, (b) The time taken for the rocket to reach its maximum height when launched at $ 180 \, \text{m/s} $.
, (c) The maximum height the rocket reaches when launched at $ 180 \, \text{m/s} $.
, (d) The velocity and time of impact (assuming that the rocket collides with the spacecraft).
:

Jason · Accepted Answer

Minimum Initial Velocity: $ 171.47 \, \text{m/s} $
Time to Maximum Height: $ 18.37 \, \text{s} $
Maximum Height Reached: $ 1,653.06 \, \text{m} $
Velocity at Impact: $ 54.76 \, \text{m/s} $ upward
Time of Impact: $ 12.78 \, \text{s} $

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