 # Kinematics and Projectile motion worksheet

Question -1
A bus start at Station A from rest with uniform acceleration 2m/sec2.Bus moves along a straight line
1. Find the distance moved by the bus in 10 sec?
2. At what time, it velocity becomes 20m/sec?
3. How much time it will take to cover a distance of 1.6km

Question -2
A object is moving along an straight line. The motion of that object is described by
x=at+bt2+ct3
where a,b,c are constants and x is in meters and t is in sec.
1. Find the displacement at t=1 sec
2. Find the velocity at t=0 and t=1 sec
3. Find the acceleration at t=0 and t=1 sec

Question 3
An object is thrown vertically upward with an initial velocity of 40m/s.Two second later another object is thrown upward with the same velocity.
Find out following
1. At what height they meet
2. what is the time when they meet
3. what are the velocities of each object when they meet
Question 4
A particle moves along the x-axis according to the following equation
x=pt(1-qt)   where p and q are constants and  p > 0, q>0.
Let take i as the unit vector across x-axis
1 Find out the velocity and acceleration vector for the particle
2. What time it will reach its initial point and what will be the total distance traversed
Question 5
A Balloon rises from rest on the ground vertically upwards with a constant acceleration g/8.An object is dropped from the balloon when it has risen to the height h.Find out the time taken by the object to reach the ground.
Question 6
A Police Motorcycle is moving on a highway with a speed vm  fires a  bullet  at at thief motorcycle speeding away in the same  direction with a speed vt(vt > vm).If the muzzle speed of the bullet is vb (vb > vt  - vm) find out  the following
1. What is the speed of the bullet with respect to the observer sitting on the ground?
2. What speed will the bullet hit the thief
3 What will the speed of the bullet with respect to another police motorcycle moving in the same direction at a speed of v
Question 7
A nut comes loose from a bolt on the bottom of the elevator as the elevator is moving up the shaft at 3 m/s. The nut strikes the bottom of the shaft in 2 sec
Find out the following
a. How far from bottom of the shaft was the elevator when the nut fell off?
b. How far above the bottom of the shaft  was the nut .25 sec after the fell off.?
c. How far above the bottom of the shaft was the elevator when the nut fell on the ground?
d. At what height above the bottom of the shaft, nut has zero velocity after the fell off?
e. what is the total distance traveled by nut in it motion after the fell off?
Given g=9.8 m/s2
Question 8
A particle moves 4 km North East and reach position A and then moves 3 Km South East to reach the position B. Let assume the initial point has co-ordinates (0, 0).And Co-ordinates of the position A and B are
A -> (xa,ya)
B -> (xb,yb)
Also i and j are the unit vector across the x and y direction
Find out the following
1. Find out the co-ordinates of Position A  and B
2. Find out the distance of point B from the Origin
3. Find out the position vector of point A and B
Question 9
An object is fired upward at an angle  400 to the horizontal .The object is fired with an initial speed of 20m/s.
Find out the following
1. How high up will it strike a wall which is 8 m away
2. How much time it will take to strike the wall
3. What are the horizontal and vertical components of velocity when it strike the wall
Question 10
The position of a particle is given by the below equation
R= (2sin2Πt)i + (3cos2Πt)j
a) Find out the trajectory of the particle
b) Find out the velocity and acceleration vector and the relation between the acceleration and position vector.
c) Find out the times when velocity becomes maximum and minimum.
d)  Find out the time dependence of the angle α etween velocity and acceleration vector
e) Find the angle α at t=0 and t=1/4
Question 11
A ball is thrown upward from a point O on the side of a hill which slopes upward uniformly at an angle 300.Intial Velocity of the ball is v0 and it is thrown at an angle 600 with respect to horizontal.
1. Find out the range along the slope of the hill
2. Find out the Time period of the Projectile
3. What height above the point  O ,ball strike the incline plane
4. What velocity does the ball strike the plane
Question 12
A particle moves in the plane xy with velocity given by v=ai+bxj where  i   and j  are the unit vectors of the x and y axis and a and b are constants. At the initial moment of time the particle was located at point x=y=0. Find
1. The equation of particle’s trajectory y(x)
2. The curvature radius of trajectory as a function of x.
Question 13
A boy is standing at a distance a1 from the foot of a tower. The boy throws an stone at a angle 45° which just touches the top of the tower and strikes the ground at a distance a2 from the point the boy is standing. Find the height of the tower
Question 14
A ball is thrown upward from a point on the side of a hill which slopes upward uniformly at angle 28°.Intial velocity of the ball is v0= 33 m/s and at an angle 65°(with respect to the horizontal. At what distance up the slope the ball strike and in what time?
Question 15
A Cannon on a level plain is aimed at an angle θ above the horizontal. A shell is fired with a muzzle velocity v0 towards a pole which is distance R away. It hits the pole at height H.
a find the time taken to reach the pole
b. find the value of H in terms of θ,R and v0
Question 16
The displacement of the body x(in meters) varies with time t (in sec) as
x=-2/3t2 +16t+2
find following
a. what is the velocity at t=0,t=1
b. what is the acceleration at t=0
c. what is the displacement at t=0
d .what will the displacement when it comes to rest
e .How much time it take to come to rest.
Question 17
A man runs at a speed at 4 m/s to overtake a standing bus. When he is 6 m behind the door at t=0,the bus moves forward and continues with constant acceleration of 1.2 m/s2
find the following
a. how long does it take for the man to gain the door
b if in the beginning he is 10m behind the door ,will he running at the same speed ever catch up bus?
Question 18
The current velocity of a river grows in proportion to the distance  from its bank and reaches its maximum v0 in the middle. The width of the river is b. The velocity near the banks is zero. A boat is so moving on the river that its velocity u relative to the water is constant and perpendicular to the current
a) Find the velocity of the current at a distance y from the bank ( y<b/2)
b) Find the velocity of the boat relative to ground at any point on it path ( y<b/2)
c) Find the velocity of the boat relative to ground at any point on it path ( b/2< y < b)
d) Find the acceleration also on both the above distances
e) Find the distance through which the boat crossing the river will be carried away by the current
f) Find the trajectory of the boat

Solutions 