Motion In A Plane CBSE Questions & Answers

A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity?

Rain is falling vertically with a speed of 30 m \({{\rm{s}}^{ - {\rm{1}}}}\). A woman rides a bicycle with a speed of 10 m \({{\rm{s}}^{ - {\rm{1}}}}\) in the north to south direction. What is the direction in which she should hold her umbrella?

A man can swim with a speed of 4.0 km/h in still water. How long does he take to cross a river 1.0 km wide if the river flows steadily at 3.0 km/h and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?

In a harbor, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbor flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?

The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m \({{\rm{s}}^{ - {\rm{1}}}}\)can go without hitting the ceiling of the hall?

A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball?

A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone?

An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity.

Which of the following statements not true?

The position of a particle is given by \(r = 3.0t\hat i - 2.0{t^2}\hat j + 4.0\hat k\) Find the velocity and acceleration of the particle.

The position of a particle is given by \(r = 3.0t\hat i - 2.0{t^2}\hat j + 4.0\hat k\) Find the magnitude and direction of velocity of the particle at t = 2.0 s.

4.21 A particle starts from the origin at t = 0 s with a velocity of 10.0 \(\hat j\) m/s and moves in the x-y plane with a constant acceleration of ( 8.0\(\hat i\) + 2.0\(\hat j\)) m \({{\rm{s}}^{ - {\rm{2}}}}\). At what time is the x- coordinate of the particle 16 m? What is the y-coordinate of the particle at that time?

An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10.0 s apart is 30\(^\circ \), what is the speed of the aircraft?

A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m \({{\rm{s}}^{ - {\rm{1}}}}\) to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit ? (Take g = 10 m\({{\rm{s}}^{ - {\rm{2}}}}\)).

A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?