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 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 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.)

time of collision is

t = 0.395 s

so they will collide at height of 5.63 m from ground

Explanation:

initial speed of the ball when it is dropped down is

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

now relative velocity of object with respect to ball

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

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

so they will collide at height of 5.63 m from ground

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answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.