A rocket is fired vertically upwards with initial velocity 80m/s at the ground level. Its engines then fire and it is accelerated at 4m/s2 until it reaches an altitude of 1000m. At that point the engines fail and the rocket goes into free-fall. Disregard air resistance.What is the velocity just before it collides with the ground? (in m/s)
The correct option is C 184
The first part of the motion is the motion with constant acceleration at 
. The initial velocity for this motion is 80 m/s. Then we can write the equation, which describes the dependence of height of the rocket on time:
From this equation we can find the time when the rocket reaches the height 1000 m = h:
The solution of this equation is 10 s. So after 10 seconds, the engine fails. The velocity at this moment of time is
After this moment of time we have free fall motion – there is only one force acting on the object (it is gravitational force) – this force provide free fall acceleration.
The initial velocity is 120 m/s pointing upward. The acceleration is 
pointing downward. The initial height of the rocket is 1000 m. Then the equations which describe this motion are the following:
To find the maximum height of the rocket we can use the last equation. The velocity at the maximum height is 0. Then
To find the time when the rocket hits the ground we need to use the first equation:
When the rocket hits the ground h=0. Then
From this equation, we can find time: 31 s.
Then we can find the time when the rocket is in the air: it is the sum of the time when it reaches 1000 m and the time when it hits the ground:
To find the speed of the rocket when it hits the ground we need to use the last equation:
When the missile hits the ground h=0. Then
The first part of the motion is the motion with constant acceleration at . The initial velocity for this motion is 80 m/s. Then we can write the equation, which describes the dependence of height of the rocket on time:
From this equation we can find the time when the rocket reaches the height 1000 m = h:
The solution of this equation is 10 s. So after 10 seconds, the engine fails. The velocity at this moment of time is
After this moment of time we have free fall motion – there is only one force acting on the object (it is gravitational force) – this force provide free fall acceleration.
The initial velocity is 120 m/s pointing upward. The acceleration is pointing downward. The initial height of the rocket is 1000 m. Then the equations which describe this motion are the following:
To find the maximum height of the rocket we can use the last equation. The velocity at the maximum height is 0. Then
To find the time when the rocket hits the ground we need to use the first equation:
When the rocket hits the ground h=0. Then
From this equation, we can find time: 31 s.
Then we can find the time when the rocket is in the air: it is the sum of the time when it reaches 1000 m and the time when it hits the ground:
To find the speed of the rocket when it hits the ground we need to use the last equation:
When the missile hits the ground h=0. Then
