The velocity of a particle is given as v=-x i+2y j-z k m/s. The magnitude of acceleration at point (1, 2, 4) is m/s2.
(2) 9
Each velocity component depends only on its own coordinate, so
ax= dvxdt= dvxdx dxdt=vx dvxdx (similarly for y, z)
ax=(-x)(-1)=x
ay=(2y)(2)=4y
az=(-z)(-1)=z
At (1, 2, 4): a=1 i+8 j+4 k
| a|= 12+82+42= 81
=9 m/s2
Answer: (2)
A boy throws a ball into air at 45 from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is m. (g = 10 m/s2)
An object is projected with kinetic energy K from a point A at an angle 60 with the horizontal. The ratio of the difference in kinetic energies at points B and C to that at point A (see figure), in the absence of air friction is : [figure]
A projectile is thrown upward at an angle 60 with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is 45 with the horizontal. The initial speed of the projectile is m/s.
A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are and respectively.
Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. T1 and T2 are the total flying times of first and second ball, respectively, then the ratio of T1 and T2 is
Two projectiles are fired from ground with same initial speeds from same point at angles (45 + ) and (45 - ) with horizontal direction. The ratio of their times of flights is
A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is : (use acceleration due to gravity g = 10 m/s2 and neglect air resistance)
If L and P represent the angular momentum and linear momentum respectively of a particle of mass 'm' having position vector as r = a( i t + j t). The direction of force is
The angle of projection of a particle is measured from the vertical axis as and the maximum height reached by the particle is hm. Here hm as function of can be presented as
A particle is projected with velocity u so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as nu225g, where value of n is: (Given, 'g' is the acceleration due to gravity.)