# Numericals from Kinematics

**PHYSICS TEST (CLASS XI) Kinematics**

- A particle is projected at 60º to the horizontal with a kinetic energy K. What is the kinetic energy at the highest point
- Which of the following statements is false for a particle moving in a circle with a constant angular speed?

(a) the velocity vector is tangent to the circle

(b) the acceleration vector is tangent to the circle

(c) the acceleration vector points to the centre of the circle

(d) the velocity and acceleration vectors are perpendicular to each other - A car is moving in a circular horizontal track of radius 10.0 m with a constant speed of 10.0m/s.A plumb bomb is suspended from the roof of the car by a light rigid rod of length1.00m. What is the angle made by the rod with the track is (g= 10 m/s²)
- The distance traveled by an object along the axes are given by x=2t², y = t² – 4, z = 3 t – 5. What is the initial velocity of the particle
- A boy playing o the roof of 10m high building throws a ball with a speed of 10 m/s at an angle of 30º the horizontal. How far from the throwing point will the ball be at the height of 10m from the ground?
- If a body travels half of its path in the last second of its fall from rest; find the time and height of its fall?
- An object A is kept fixed at the point x = 3m and y=1.25m on a moving along the +x direction with an acceleration 1.5 m/s. At the same instant a stone hitting the object during its downward motion at an angle pf 45º to the horizontal .all the motions are in X-Y plane .Find u and time after which stone hits the object. Take g = 10m/s²
- Three particles a, b and c are situated at the vertices of an equilateral triangle ABC of side d at t=0. Each of the particles moves with constant speed v. A always has its velocity along BC and C along CA. At what time will the particles meet each other?
- A man standing on road has to hold his umbrella at 30º with the vertical to keep the rain away he throws the umbrella and starts running at 10 km/h. he finds that raindrops with respect to [a]the road, [b] the moving man.

10. A man can swim at speed of 3 km/h in still water. He wants to cross a 500 m wide river flowing at 2 km/h. he keeps himself always at an angle of 120º with the river flow while swimming. (a) Find the time he takes to cross river. (b) At what point on the opposite bank will he arrive?

11. A staircase contains three steps each 10cm high and 20 cm wide what should be the minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directly the lowest plane?

12. A person is standing on a truck moving with a constant velocity of 14.7 m/s on a horizontal road .The man throws a ball in such a way that it returns to the truck after the truck has moved 58.8 m .find speed and the angle of projections

(a) as seen from the truck, (b) as seen from the road

13. An airplane has to go from a point A to another point B, 500 km away due 30º east of

north. a wind is blowing due north at a speed of 20 m/s (a) find the direction in which the pilot should head the plane to reach the time taken by the plane to go from A to B

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