A curve is described by the following parametric equations
Determine the unit tangent vector to the curve at the point .
The position vector of the curve is r(t) = ⟨2 cos t, 2 sin t, cos(3t)⟩. The tangent vector to the curve is obtained by differentiating r(t) ___ ________ _________ _________ _________ ______.
________ _______ _______ ___ ____.
__________ _______ ______ __________ ____.
_____ ____ ___ _____ _____ ________ ________ ___.
______ ______ _____ ___ ______ ____ _______ _____ _____ _________ _______.
___ _________ _____ ____ __________ ______ ___.
____ _____ ________ ____ _________.
___ _________ ______ ___ ____ ______.
________ _________ ______ _________ ______ _____ ________ ____ _________ __________.
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An person jumping from a height of
hits the ground with a speed of nearly
. Calculate the impulse experienced by the person during the collision with ground and the average force exerted on the person, if the collision with the ground lasts for
.
An object undergoes SHM with frequency . The initial displacement is
and the initial velocity is
. Calculate the amplitude, maximum velocity and maximum acceleration of the object.
Restoring and frictional forces of magnitudes kx and , respectively act simultaneously on an object of mass
attached to a spring. Under the influence of these forces, the mass oscillates with a frequency
and its amplitude reduces to half in
. Calculate the damping constant
, the force constant k and the damping factor b. Also write the differential equation for the system.
A block of mass is moved up from the base a rough inclined plane making an angle of
with the horizontal with initial speed
. The coefficient of kinetic friction between the block and the plane is 0.2. Calculate
i) the maximum distance the block travels up the incline before coming to rest.
ii) the speed of the block when it returns to the base of the inclined plane.
iii) the energy lost over the entire motion. Take .
क) तीन सदिश ,
और
प्रतिबंध
को संतुष्ट करते हैं। यदि
और
तो
का मान ज्ञात करें।
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इस तरंग की संचरण दिशा निर्धारित करें तथा इसका आयाम, तरंग संख्या, तरंगदैर्घ्य एवं आवृत्ति परिकलित करें।
A particle A of mass moving along the x-axis with speed
collides elastically with a particle B of equal mass which is initially at rest. After the collision, particle A moves at an angle of
above the x-axis. Calculate the velocities of the two particles after the collision.