Mechanics | Relativity Answers

Problem:
A baseball is hit toward center field; it will travel 72 m before it reaches the ground. At the first moment the ball is hit, the center fielder is 98 m away from home plate. He uses 0.5 s to judge the flight of the ball, then races to catch it. The ball’s speed when it leaves the bat is 35 m/s at home plate. Can the center fielder catch the ball before it hits the ground?

A heavy stone hanging from a massless string of length 15 m is projected horizontally with speed 147 m/s. The speed of the particle at the point where the tension in the string equals the weight of the particle is :

A stone tied to the end of 20 cm long string is whirled in a horizontal circle. If the centripetal acceleration is 9.8 ms-2, its angular speed in radian per sec is :

A person aiming to reach exactly opposite point on the bank of a stream is swimming with a speed of 0.5 m/s at an angle of 120 degree with the direction of the flow of the water. The speed of water in the stream is
(1)0.25 m/s
(2)0.5 m/s
(3)1.0 m/s
(4)0.433 m/s

The speed of a boat is 5 km/hr in still water. It crosses a river of width 1.0 m along the shortest possible path in 15 minute. The velocity of the river water (km/h) is
(1) 3
(2) 1
(3) 4
(4) 5

A student walks forward a distance represented by the displacement vector A of magnitude 6.2 m, and then walks to obtain an additional displacement B of length 4.1 perpendicular to A. (a) What is the magnitude of the resulting displacement from the origin? (b) What magnitude of total displacement would result if the second displacement were -B instead of B?

A small block of mass m is kept on a bigger block of
mass M which is attached to a vertical spring of spring
constant k as shown in the figure. The system oscillates
vertically. (a) Find the resultant force on the smaller
block when it is displaced through a distance x above
its equilibrium position. (b) Find the normal force on the
smaller block at this position. When is this force smallest
in magnitude ? (c) What can be the maximum amplitude
with which the two blocks may oscillate together ?

In a collision, two trolleys stick together. What is their velocity after the collision?

BEFORE COLLISION: CART 1( 1500kg moving forward at 2m/s) CART 2( 2000kg moving backwards at -3m/s)

AFTER COLLISION: 1500kg+2000kg together.

What is their velocity after the collision?

A hemispherical bowl of radius R is rotated about its
axis of symmetry which is kept vertical. A small block
is kept in the bowl at a position where the radius makes
an angle 0 with the vertical. The block rotates with the
bowl without any slipping. The friction coefficient
between the block and the bowl surface is u. Find the
range of the angular speed for which the block will not
slip.

21. A block of mass m is kept on a horizontal ruler. The
friction coefficient between the ruler and the block is g.
The ruler is fixed at one end and the block is at a
distance L from the fixed end. The ruler is rotated about
the fixed end in the horizontal plane through the fixed
end. (a) What can the maximum angular speed be for
which the block does not slip ? (b) If the angular speed
of the ruler is uniformly increased from zero at an
angular acceleration a, at what angular speed will the
block slip ?