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Zepler [3.9K]
3 years ago
12

In Example 2.12, two circus performers rehearse a trick in which a ball and a dart collide. Horatio stands on a platform 6.4 m a

bove 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 16.2 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.)
Physics
1 answer:
pickupchik [31]3 years ago
4 0

Answer:

time of collision is

t = 0.395 s

h = 5.63 m

so they will collide at height of 5.63 m from ground

Explanation:

initial speed of the ball when it is dropped down is

v_1 = 0

similarly initial speed of the object which is projected by spring is given as

v_2 = 16.2 m/s

now relative velocity of object with respect to ball

v_r = 16.2 m/s

now since we know that both are moving under gravity so their relative acceleration is ZERO and the relative distance between them is 6.4 m

d = v_r t

6.4 = 16.2 t

t = 0.395 m

Now the height attained by the object in the same time is given as

h = v_2 t - \frac{1}{2}gt^2

h = 16.2(0.395) - \frac{1}{2}(9.81).395^2

h = 5.63 m

so they will collide at height of 5.63 m from ground

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