1 A rocket, mitially at rest on the ground, accelerates vertically. Il accelerales uniformly until it reaches a speed of 900 m/s after 30$ After this period of uniform acceleration the rockel engine cuts out. During the next 90s, the upward speed of the rocket decreases uniformly to zero (a) On Fig. 4. 1. plot a speed lime graph for the rocket for the first 120s of its flight reed m/s time/s Fig. 4.1 (b) Using the graph, (1) calculate the acceleration during the first 30 s. [2] acceleration =
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Answer:
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 O. 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 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
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