Problems with video solutions

CH02-01

A physical quantity is described by the relation a^1/2 b^2 c^3 d^-4. If the respective relative errors are 2%, 1%, 3% and 5% find the relative error of the quantity. Your answer in XX %

CH02-02

Express mass as a function of time t (i.e. units are T), velocity c [i.e. units are L T-1] and angular momentum h [i.e. units are M L2 T-1]

CH02-03

The position vector of a particle is given by r=3t2 (i) + 4t2 (j) + 7 (k). Find the distance traveled the first 10 s. Your answer in XXX m

CH02-04

Find the magnitude of the vector 2(i)+3(j) along the directions of (i+j) and (i-j). Your answer in X.X

CH02-05

The height reached in time by an object thrown with speed u is given by h=ut-1/2 gt^2. Find the time that it takes to reach maximum height. Use u=10 and g =9.8 ms-2. Your answer in X.XX s

CH03-01

A ball falls from 20 m height on the floor and rebounds to 5m. The time of contact is 0.02 s. Find the acceleration during impact. Your answer in XXXX ms-2

CH03-02

A stone is thrown from rest down a well. Five seconds later you hear the splash. How deep is the well? (speed sound ~341 ms-1)

CH03-03

A balloon starts rising from the ground with acceleration of 1.25 ms-2. After 8 s a stone is released from the balloon. What is the maximum height the stone will reach?

CH03-04

You walk up an escalator that is stationary in 15 s. If the escalator is moving and you stand still you cover the same distance in 18 sec. How much time will it take you to walk up the escalator if you and the escalator are moving? Your answer in X.X s

CH03-05

From a tower of height H a stone is thrown upwards with speed 10 ms^-1. The time taken for the stone to hit the ground (from the moment it leaves our hand) is N times the time is takes to reach the highest point in its trajectory. Find H when N=10 and gravity is considered 9.8 ms-2

CH03-06

Two trucks move at constant speeds u1=10 ms-1 and u2=8 ms-1 from town A to town B on a straight line. The first arrives at noon (12:00) and the second one minute later. Find the distance between A and B. Your answer in X.X km

CH03-07

The velocity of an object is v=At+Bt^2. Find the distance traveled between 1s and 2s if A=2 ms-2 and B=4 ms-3

CH03-08

The motion of falling body from rest in a resisting medium is described by dv/dt=A-Bv. Find the velocity when A=5, B=2 and after 10 seconds have elapsed

CH04-01

The x and y coordinates of the particle at any time are x=5t-2t^2 and y=10t where x and y are in meters and t in seconds. Find the acceleration at t=2 s

CH04-02

The position of a particle moving in the x-y plane at any time is given by x=3t^2-6t and y=t^2-2t in meters. Find the magnitude of the velocity at t=1 s

CH04-03

Is given by r=3.0 t (i) – 2.0 t^2 (j) + 4.0 (k) in meters. Find the magnitude of its velocity at t=2s

CH04-04

A projectile is given an initial velocity of (i+2j) ms-1 where I is a vector along the ground and j in the vertical. Find its position along the y-axis when x=1 m

CH04-05

A projectile is launched from the top of inclined plane of angle 45° with an initial speed of 60 ms-1. The projectile land at the bottom of the plane. Find the distance covered by the projectile along the inclined plane. Your answer in XXXX m

CH04-06

The launching speed of a projectile is five times the speed it has at its maximum height. Find the elevation angle during launching

CH04-07

An open umbrella is held upright and rotated about the handle at a uniform rate of 21revolution in 10 s. If the rim of the umbrella is a circle of 0.5 m radius and the height of the rim above ground is 1.5 m, then the drops of water spinning off the rim will hit the ground from center of umbrella, at a distance of:

CH05_06-01

A body of mass 400 kg is suspended at the lower end of a light vertical chain and is pulled up vertically (see fig). Initially the body is at rest and the pull on the chain is 6000·g Newton (g is grav.acc and the “pull” may be considered as the Tension on the chain ). The pull becomes smaller at a rate of 360 ·g per each meter the body is raised. Find its velocity when it has been raised by 10 m.

CH05_06-02

Two blocks A and B of masses 3m and m are connected by massless and inextensible string as shown. The system is suspended by a spring. Find the acceleration of block A right after the string is cut. Your answer in X.X ms-2

CH05_06-03

The rear side of a truck is open and a box of mass 20 kg is placed on the truck 4 m away from the open end. If p is 0.15 and g = 10 m s-² and the truck starts from rest with an acceleration of 2 m s -² on a straight road, then the box will fall off the truck when it is at a distance of x meters from the starting point. Find x. Your answer in meters XX

CH05_06-04

Two fixed frictionless inclined planes have angles 30 and 60 degrees as shown. Blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B? Your answer in X.X ms-2

CH05_06-05

Block A of mass m and block B of mass 2m are placed on a fixed triangular wedge by means of a massless, inextensible string and a frictionless pulley as shown in the figure. The wedge is inclined at 45° to the horizontal on both the sides. If the coefficient of friction between the block A and the wedge is 2/3 and that between the block B and the wedge is 1/3. Both A and B are released from rest, the acceleration of A will be

CH05_06-06

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev. per min in a horizontal plane. What is the tension in the string?

CH05_06-07

A body of mass 1 kg begins to move under the action of a time dependent force F=2t (i) + 3t² (j) N. What power will be developed after time t=2 s? Your answer in XXX W

CH05_06-08

A sphere of know mass is hanging from a string on an incline of known angle φ as shown. Find the tension (note that the string is horizontal). Take m=1 kg, g=10 ms^-2 and φ=30°. Your answer in X.X N

CH07_08-01

The target box is 2.20m horizontally from the edge of the table; see Fig. We compresses the spring 1.10 cm, but the center of the marble falls 27.0 cm short of the center of the box. How far should we compress the spring to score a direct hit?

CH07_08-02

A 10.0kg block is released from point A as shown in Fig. The track is friction- less except for the portion BC, of length 6.00m. The block travels down the track, hits a spring of force constant k = 2250N/m, and compresses it 0.300m from its equilibrium position before coming to rest momentarily. Determine the coefficient of kinetic friction between surface BC and block.

CH07_08-03

The blades of a windmill sweep out a circle of area. The wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time /?. Assume that the windmill converts 25% of the winds energy into electrical energy and that A = 30 m², v = 36 km h ¹ and the density of air is 1.2 kg m \ What is the electrical power produced?

CH07_08-04

An object of mass 10-2 kg is moving and experiences a frictional force F=-k v2. Its initial speed is v0=10 ms-1. If after 10 s its energy is 1/8 m v02 find the value of k

CH07_08-05

A running man has half the kinetic energy than that of a boy of half of his mass. The man speed up by 1 m s' and then has the same kinetic energy as the boy. What was the original speed of the man?

CH07_08-06

The world record in the Olympic games for javelin is about 98 m. If the javelin mass is 0.8 kg and the air resistance is negligible what is the average force exerted by the athlete on the javelin over a distance of 2 meters (Assume that the athlete throws at 45° angle to achieve maximum range)

CH07_08-07

A particle is projected with a velocity 20 m/s, so that it just clears two walls of equal height 10 m, which are same at a distance 20 m from each other. Find the time that it takes to travel between the walls. Your answer in X.X s

CH09-01

A 2 Kg particle has velocity of 2(i) – (j) ms-1 and a 3 kg particle has velocity of (i) + 6(j) ms-1. Find the magnitude of the total momentum of the system. Your answer in XX.XX kg m s-1

CH09-02

A ball is thrown horizontally from height 2 m and initial speed 10 (i) ms-1. The coefficient of restitution between ball and ground is 0.8. Find the height after the first rebound.

CH09-03

A radioactive nucleus of mass 4 10^-25 kg moves at a speed of 10^6 ms-1 and splits into 2 pieces of mass 1.7 10^-25 kg and 2.3 10^-25 kg. The lighter particle keeps on moving at a 25° (measured counter clockwise with the horizontal) and the other a 70° (measured clockwise with the horizontal). What is the change in kinetic energy during this process?

CH09-04

A 80 kg person stands on a 20 kg boat. The person is initially 6.1 m from the shore. He walks 2.4 m on the boat (towards the shore). Assuming no frictions, how far is the person from the shore now? Your answer in X.XX m

CH09-05

A firework of mass M breaks into 2 pieces, M/2 and 3M/4 at a horizontal distance 10 m from the launching point. The lighter piece returns back to the launching position. How far from the launching position will the heavier piece reach? Solve for M=2 kg. Your answer in XX.X

CH09-06

A 500 kg object is towed by a strong cable that delivers a force that varies with time as 400 t2. If the static and kinetic friction coefficients are 0.5 and 0.4 respectively, find the speed of the wall at t=5 s. Your answer in XX.X m s-1

CH09-07

A crate of mass 10 kg slides along 3.5 m on a free-rolling ramp of 30° of mass 40 kg (i.e. the ramp has wheels). Find the speed of the ramp when the crate reaches the bottom of the ramp (i.e. 3.5 m). Your answer in X.X ms-1

CH09-08

A block of mass m moving with speed u on smooth horizontal surface towards stationary wedge of the same mass. How high will the block climb on the wedge? Solve for m=10 kg, u=2 ms-1 and g=9.8 ms-2. Your answer in X.X m

CH09-09

Show that the angle in a 2-D collision between two equal masses, will always be 90 °. Assume that one mass is initially stationary and both masses after the collision are moving