Consider the motion of particle mass m and charge q in an electromagnetic field with
electric field vector is E and the magnetic field vector is B. The force acting on the particle is
given by the Lorentz equation F = qE + qv x B (assuming non-relativistic case, v<<c).
(a) If there is no electric field and the particle enters the magnetic field in a direction
perpendicular to the lines of magnetic flux, show that the trajectory is a circle with radius

Human will be heading for Mars by 2030. There are already increasing number of
unmanned missions to date, with all methods of landing on Mars have required an aero-shell
and parachute sequence, by knowing the details of Mars atmosphere and surface. Consider
a Mars lander (as particle) of mass m whose motion starts from rest at an altitude ro in a
constant Mars gravitation field gM. If a resisting force F = -kmv2 is encountered, calculate the
distance s the lander falls in accelerating from zero velocity to v. Use this analysis to discuss
about one particular failed landing which resulted in the lander Schiaparelli crashing to the
surface at 340 mph due to miscalculation of Mars descent.

a proton undergo a head on elastic collision with a particle of unknown mass which is initially at rest and rebounds with 4/9 of its initial kinetic energy. Calculate the ratio of the unknown mass with respect to the mass of proton.

Please if the velocities are unequal how exactly do you show that kinetic energies are equal at the finish line? Could you please show with workings....

A car of mass 1200kg traveling westward at 30. M/s is slowed to a stop in a distance of 50. M by the cars brakes. What was the breaking force?

The kinetic energy of a mass is given by ½MV² of its speed is doubled by what factor does the energy change

Pirate Jack is in a speed boat cruising along. He is going to jump off the boat at 7 m/s and onto the tube at the same height as the boat and being pulled 4 m behind. What angle does he have to jump at?

A basketballer is trying to make a shot in an international game from the 3 point line (6.75 m
away from the hoop). The basketball hoop is 3.05 m above the floor, the basketballer’s hands
are 1.95 m above the floor when they release the ball at an angle of 39° above the horizontal.
What velocity would the ball have to have been thrown with to reach and fall down into the
hoop? And if the ball has a mass of 625 g what was the ball’s maximum potential energy during
the throw?

Two boys are racing for chocolates. The older one has a speed of 1.0 m/s and the younger one has a 0.50 m/s. The older one told the younger one to run first, which the younger one does. Ten seconds later the older one follows. How far would they be from the starting line for the older one to overtake the younger one.

Two iceboats A and B race on a frictionless lake. A has a mass and of m and B has mass of 2m. The wind exerts a constant force F on both boats along their direction of motion. Both boats start from rest , and both travel at the same distance s to finish line.At the finish line the speed of A is (a)equal to the speed of B
(b)greater than the speed of B
(c)less than the speed design of B
(d) cannot be obtained from the information given
Explanation of answer please