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. : "Motion_2D"

Motion In A Plane

Q- A small ball is suspended from point A by a thread of length L.  A nail is driven into the wall at a distance of L/2 below A, at O.  The ball is drawn so that the thread takes up a horizontal position.

(a) At what point in the ball’s trajectory will the tension in the thread disappear?
(b)…

Kinematics: Projectile Motion

Q- A rocket is fired at an angle of 600 with horizontal and accelerates in a straight line at 25ms-2 for 2.5s before the rocket motor stops and it eventually falls to the ground. Neglecting air resistance

(a) Make a labelled sketch of the rockets trajectory starting from the launch point. Include …

Relative Motion

Q- A boat which can travel at 12.5 m/s in still water needs to travel West across a river with a current of 8.4 m/s flowing South.

(a) What heading must the boat take in order to travel West relative to the shore? Draw a diagram.

(b) What will be the boat’s velocity relative to the shore?

Solut…

Projectile Motion

Q- A shall is fired from a hill of height ‘h’ at an angle of 450.  What is the magnitude of its velocity of projection as a function of its horizontal distance covered on ground x, acceleration due to gravity g and height h?

Solution:

Projectile Motion

Q- A projectile is fired form the edge of a 100 meter tall building with an initial speed of 10 m/s at 30 degrees above the horizon and lands on the ground. Neglecting the air resistance.

(a) Find the horizontal and vertical components of the initial velocity of the projectile.

(b) How long doe…

Circular Motion

Q- A cat rides a merry-to-round turning in circular motion with uniform speed. At time t1 = 2.00 s, the cat’s velocity (in m/s) is V1=3.0 i + 4.0 j, measured on a horizontal x-y coordinate system. At t2 = 5.00 s its velocity is V2= (-3.0) i + (-4.0) j. What are the

(a) magnitude of the cat’s ce…

Motion in 2D: Relative Velocity

Q1- Two particles 1 and 2 move with constant velocities v1 and v2. At the initial moment, their radius vectors are r1 and r2. How must these four vectors be interrelated for the particles to collide?

Q2- A ship moving along the equator to the east with velocity v0 = 30 km/hr. The south-eastern wi…

Projectile Motion

(On request - Tamanna)

Q- A ball is thrown vertically upward from a window at 10 m/s at an angle of 45° to the horizontal. It hits the ground 5.0 s later.
a) What is the vertical height of the window from the ground?
b) How far from the base of the building does the ball strike the ground?

Projectile Motion

Q- An artillery shell is fired with an initial velocity of 300 m/s at 60 degrees above the horizontal. It explodes 40.0s after firing. What are the x and y coordinates of the shell where it explodes relative to its firing point?

Solution:

Motion in 2 D: Relative velocity

Q- A boat is trying to get from point A to point B, which is exactly to the east of A. The ocean current is due north at 4.8 km/h. The boat speed relative to the water is 18 km/h.

a) If the captain heads his boat due east, what will be his actual course relative to the shore?

b) To attain a stra…

Circular Motion

Q- The drive train of a bicycle has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady cadence of 76.0 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter.

(a) Calculate the speed of a link of the chain r…

Projectile Motion

Q- An airplane with a speed of 75 m/s is climbing upward at an angle of 30.0 ° with respect to the horizontal. When the plane's altitude is 600 m, the pilot releases a package.

(a) Calculate the distance along the ground, measured from a point directly beneath the point of release, to where the …

Projectile Motion

Q- A marble is thrown horizontally with a speed of 20 m/s from the top of a building. When it strikes the ground, the marble has a velocity that makes an angle of 37 ° with the horizontal. From what height above the ground was the marble thrown?

Solution:

Projectile Motion

Q- In the javelin throw at a track-and-field event, the javelin is launched at a speed of 40.0 m/s at an angle of 37° above the horizontal. As the javelin travels upward, its velocity points above the horizontal at an angle that decreases as time passes. How much time is required for the angle to be…

Motion in 2D - Aircraft in wind

Q- The airport B is due north of airport A. On a particular day the velocity of wind is (80i+25j) km/h. Relative to the air an aircraft flies with constant speed 208 km/h. When the aircraft flies directly from A to B
(a) Show its speed relative to the ground is 217km/h
(b)After flying from A to B th…

Projectile Motion

Q- A baseball is hit into the air at an initial speed of 30 m/s and an angle of 60° above the horizontal. At the same time, the center fielder starts running towards the batter and catches the ball 1 m above the level at which it was hit. If the center fielder is initially 1.25 x 102 m from home pl…

Motion in 2D - Collision

Q- Particles of masses m1 = 3kg and m2 = 5kg move on a collision course with velocities: u1 = (7 i + 3 j) m/s and u2 = (3 i + 7 j) m/s, respectively. After they collide, their velocities are v1 = (a i + b j) m/s and v2 = (c i + 4 j) m/s, respectively. If the collision is perfectly elastic, determine…

Projectile Motion

Q- A ball is thrown at 20 m/s at an angle of 300 to the horizontal. It is thrown in the direction of a wall which is 5m away on the ground, and 2m high. Does the ball go over the wall, or does it collide with the wall?

Solution:

Projectile Motion

Q- Suppose the water at the top of Niagara Falls has a horizontal speed of 3.00 m/s just before it cascades over the edge of the falls. At what vertical distance below the edge does the velocity vector of the water point 60.0° below the horizontal?

Solution:

Projectile Motion

Q- A builder throws tiles weighing 1.5 Kg horizontally at a speed of 1m/s from a roof 30m high

(a) How far away from the house will the tiles land?

(b) What is the speed of a tile as it hits the ground?

(c) What is the kinetic energy of the tile at ground level?

Solution:

20 .