In a local bar, a customer slides an empty beer mug down the counter for a refill. the height of the counter is 1.20 m. the mug slides off the counter and strikes the floor 1.60 m from the base of the counter.

(a) with what velocity did the mug leave the counter?
m/s

(b) what was the direction of the mug's velocity just before it hit the floor?
° (below the horizontal)

Answer

given,

height of counter = 1.20 m

horizontal distance from base = 1.6 m

a) velocity of mug = ?

   using equation of motion

     t = 0.495 s

 speed of the mug

      s_x = v x t

     1.6 = v x 0.495

      v = 3.23 m/s

b) final velocity of mug in y direction

      again using equation of motion

      v² = u² + 2 a s

      v²= 0 + 2 x 9.8 x 1.2

      v = √23.52

      v_y = 4.85 m/s

now, direction

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.