x (m) Position as a function of time t 4.00 s 20 00 04 0.8 12 16 20 24 2.8 3.2 3
ID: 1879054 • Letter: X
Question
x (m) Position as a function of time t 4.00 s 20 00 04 0.8 12 16 20 24 2.8 3.2 3.6 4.0 v (m/s) (mIS Velocity as a function of time 20 6 2.0 24 6 4.0 20 a (is)Acceleration as a function of time 10 04 08 1.2 16 24 2.8 3.2 36 4.0 10 Ploy Pause S0 StepRese This is a simulation of the mation or a ball that has a rocket engine mounted underneath it. The ball is released from rest trom a height of 40 meters above the ground, and it falls 20 meters under the inluence of gravity alone. At that point, the rocket engine kicks in, giving the ball an upward acceleration of 10 mysys (as opposed to the acceleration downward of 10 m/s/s that it just had). You can see the ball's motion diagram, with the position marked at 0.5 s intervals, as well as graphs of the ball's position, velocity, and acceleration, all as a function of time. The simulation shows the ball being relcased trom a height of 40 m above the ground. Now, we want you to do thesc calculations for the situation when the ball starts 56.0 m above the ground. As in the simulation, the ball drops in free fall (g 10 msis down) for haif that distance, and then the rocket engine comes on, giving a net acceleraticn of 10 mys's up, for the remaining half of the distance. (a) Whan the ball starts 66.0 m above the ground, and the motion proceeds as described above, what is the total time it will take to reach the ground (C) What is the maximum speed the ball reaches in its moion?Explanation / Answer
a- time taken to assend first 33m can be found out by formula s=ut+.5at2
where s id distance travelled
u is the initial velocity
t is the time taken
and a is the accn of the object
therefore, 33=0*t + .5*10*t2
33/5=t2
t=2.56 sec
and velocity when assended 33m
v2=u2+2as
v2=2*10*33
v=(660).5
hence time to assend another 33m is equal to,
0=(660).5-10*t
t= 2.56 sec
hence total time taken to assend 66m=5.12 sec
b- max velocity will be just before when accn changes
which is (660).5
= 25.6 m/s2
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