A ball is hit 1 meter above the ground with an initial speed of 40 m/s. If the ball is hit at an angle of 30 above the horizontal, when will the ball hit the ground?

Explanation:

Given:

height above the horizontal form where the ball is hit,

angle of projectile above the horizontal,

initial speed of the projectile,

Firstly we find the vertical component of the initial velocity:

During the course of ascend in height of the ball when it reaches the maximum height then its vertical component of the velocity becomes zero.

So final vertical velocity during the course of ascend:

Using eq. of motion:

(-ve sign means that the direction of velocity is opposite to the direction of acceleration)

(from the height where it is thrown)

Now we find the time taken to ascend to this height:

Time taken to descent the total height:

Now the total time taken by the ball to hit the ground:

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.