Honors Physics Fall Exam 2014
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circus juggler performs an act with balls that he tosses with his right hand and catches with his left had. Each ball is launched at an angle of 75° and reaches a maximum height 88 cm above the launching height. If it takes the juggler 0.2 s to catch a ball with his left hand, pass to his right hand and toss it back into the air, what is the marimum number of balls he can juggle?
3 answers
Honors Physics Fall Exam 2014
I think you are really asking how long does it take to go up 0.88 meters and how long to come back down. This is presumably on earth where the acceleration due to gravity is -9.81 m/s^2
So what was initial velocity component upward?
(1/2)m Vi^2 = m g h conservation of energy
Vi = sqrt (2 g h)
= sqrt (2 *9.81*.88)
= 4.16 meters/second
now the AVERAGE speed upward is half of that so
Vav = 2.08 m/s
so the time to rise .88 meters is
trise = 0.88/2.08 = 0.424 seconds
fall time is the same so the total time in the air for this toss is
0.847 second
So what was initial velocity component upward?
(1/2)m Vi^2 = m g h conservation of energy
Vi = sqrt (2 g h)
= sqrt (2 *9.81*.88)
= 4.16 meters/second
now the AVERAGE speed upward is half of that so
Vav = 2.08 m/s
so the time to rise .88 meters is
trise = 0.88/2.08 = 0.424 seconds
fall time is the same so the total time in the air for this toss is
0.847 second