In Example 2.12, two circus performers rehearse a trick in which a ball and a dart...

 

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In Example 2.12, two circus performers rehearse a trick in which a ball and a dart collide. Horatio stands on a platform 8.4 m above the ground and drops a ball straight down. At the same moment, Amelia uses a spring-loaded device on the ground to launch a dart straight up toward the ball. The dart is launched at 10.4 m/s. Find the time and height of the collision by simultaneously solving the equations for the ball and the dart. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) time height Did you accidentally divide or take the inverse in your calculation? s m In Example 2.12, two circus performers rehearse a trick in which a ball and a dart collide. Horatio stands on a platform 8.4 m above the ground and drops a ball straight down. At the same moment, Amelia uses a spring-loaded device on the ground to launch a dart straight up toward the ball. The dart is launched at 10.4 m/s. Find the time and height of the collision by simultaneously solving the equations for the ball and the dart. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) time height Did you accidentally divide or take the inverse in your calculation? s m

Answer rating: 100% (QA)

SOLUTION To solve this problem we need to find the time and height of the collision by simultaneously solving the equations for the ball and the dart Lets start by writing the equation of motion for the ball y y0 v0t 12gt2 where y is the height of the ball y0 is the initial height which is 0 since Horatio drops the ball from rest v0 is the initial velocity which is 0 since the ball is dropped from rest t is time and g is the acceleration due to gravity which is 98 ms2 Now lets write the equation of motion for the dart y y0 v0t 12gt2 where y is the height of the dart y0 is the initial height which is 0 since Amelia launches the dart from the ground v0 is the initial velocity which is 104 ms t is time and g is the acceleration due to gravity We want to find the time and height of the collision so we set up a system of equations using the two equations above y 0 balls initial height y 0 darts initial height v0t 12gt2 0 balls equation of motion v0t 12gt2 104 ms darts equation of motion Now we can solve this system of equations First we can solve the first equation for t ... View the full answer