Mechanics | Relativity Answers

A football is launched at an angle such that the vertical component of its velocity and the horizontal component of its velocity are both equal to 40 m/s.
How long does it take for the football to reach its highest point?
What horizontal distance does the football travel in this time?

A medieval castle occupant takes a dislike to some armed visitors who are at the foot of the castle wall and drops a rock towards them if the wall is 19m high and the receivers only stands 1.6m tall how much time do they have to move aside before the rock hits one of their heads? How fast will the rock be moving if a succesful impact is made?

A car of mass 1000 kg moving witha velocity of 90 km/h collides with a tree and comes to stop in 10 s. What is the change in momentum of the car? What is the force applied by the tree to stop the car?

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.

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?

A train travels between station 1 and 2, the engineer of the train is instructed to start from rest at station 1 and accelerate uniformly between points A and B, then coast with a uniform velocity between points B and C, and finally accelerate uniformly between points C and D until the train stops at station 2. The distances AB, BC, and CD are all equal, and it takes 5 minutes to travel between the two stations. Assume that the uniform accelerations have the same magnitude, even when they are in opposite directions.
a.) How much of this 5 minute period does the train spend traveling between points A and B?
b.)How much of this 5 minute period does the train spend traveling between points B and C?
c.) How much of this 5 minute period does the train spend traveling between points C and D?

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?