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A ball rolls off the end of an incline with a vertical velocity of 20 cm/s downward, and a horizontal velocity of 80 cm/s. The ball falls freely to the floor 120 cm below.
• For the interval between the end of the ramp and the floor, hat are the ball's initial velocity, displacement and acceleration in the vertical direction?
The ball’s initial velocity is 20cm/sec. The ball’s displacement is 120cm. The ball’s acceleration due to gravity is 980cm/sec^2. All of these are given.
• What therefore are its final velocity, displacement, change in velocity and average velocity in the vertical direction?
The displacement is 120cm. The final velocity is calculated using this equation:
Vf^2 = v0^2 + 2a*’ds
Vf^2 = (20cm/sec)^2 + 2(980cm/sec^2)*120cm
Vf^2 = 400 + 235,200
Vf^2 = 235,600
Vf = 485.4cm/sec
vAve is calculated this way:
vAve = (v0+vf)/2
vAve = (20cm/sec+485.4cm/sec)/2
vAve = 252.7cm/sec
Change in velocity = vf – v0
Change in velocity = 485.4cm/sec – 20cm/sec
Change in velocity = 465.4cm/sec
• What are the ball's acceleration and initial velocity in the horizontal direction, and what is the change in clock time, during this interval?
The clock time will be the same in the vertical direction so I can use vertical calculations to solve that.
‘ds = vAve * ‘dt
120cm = 252.7cm/sec * ‘dt
‘dt = 0.475sec
The acceleration is 0cm/sec, so the initial velocity is 80cm/sec
• What therefore are its displacement, final velocity, average velocity and change in velocity in the horizontal direction during this interval?
The ball’s accelerating is 0, which means that horizontally the ball is always traveling at 80cm/sec. That goes for initial velocity, final, and average. The displacement is calculated using the time I calculated earlier.
‘ds = vAve * ‘dt
‘ds = 80cm/sec * 0.4755sec
‘ds = 38.04 cm
• After the instant of impact with the floor, can we expect that the ball will be uniformly accelerated?
The ball will be uniformly accelerated because it will be traveling in 1 direction and the ball will slow down due to friction with the ground.
• Why does this analysis stop at the instant of impact with the floor?
When the ball hits the floor many new things can happen.
Right. The main point is that acceleration changes, so the equations of uniformly accelerated motion and results obtained from the equations cease to apply.
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30 minutes
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&#Good work. See my notes and let me know if you have questions. &#