passenger arriving in a new town wishes to go from the station to a hotel located km away on a straight road from the station. A dishonest cabman takes him along a circuitous path km long and reaches the hotel in min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity ? Are the two equal ?
. The ceiling of a long hall is m high. What is the maximum horizontal distance that a ball thrown with a speed of m s - can go without hitting the ceiling of the hall ? .
A cricketer can throw a ball to a maximum horizontal distance of m. How much high above the ground can the cricketer throw the same ball ? Q Fig. .
. A stone tied to the end of a string cm long is whirled in a horizontal circle with a constant speed. If the stone makes revolutions in s, what is the magnitude and direction of acceleration of the stone ? .
An aircraft executes a horizontal loop of radius . km with a steady speed of km/h. Compare its centripetal acceleration with the acceleration due to gravity. .
Read each statement below carefully and state, with reasons, if it is true or false : (a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre (b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point (c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector . The position of a particle is given by . . .
where t is in seconds and the coefficients have the proper units for r to be in metres. (a) Find the v and a of the particle? (b) What is the magnitude and direction of velocity of the particle at t = . s ?