Aball is launched from the ground at an angle of 45° with an initial velocity of 19.7 m/s. (a) what is its velocity at the top of the trajectory? (remember that it has both and x and y components when it leaves the ground) (b) what is its maximum height? (c) what is its range? (d) how long was it in the air?

Explanation:

Given that,

Initial velocity = 19.7 m/s

Angle = 45°

(a). We need to calculate the velocity at the top of the trajectory

Using formula of velocity at the top of the trajectory

Put the value into the formula

The top of the trajectory is 13.93 m/s.

(b). We need to calculate the maximum height

Using formula of height

Put the value into the formula

The maximum height is 9.90 m.

(c). We need to calculate the range

Using formula of range

Put the value into the formula

The range is 39.6 m.

(d). We need to calculate the time

Using formula of time

Put the value in to the formula

The time is 2.84 sec.

Hence, This is the required solution.

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.