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Kinematics Numerical

  1. A particle travels 20 m in 7th second and 24m in 9th sec. find initial velocity?
  2. in a projectile motion , a body thrown from the ground ,at what angle both the vertical height and range will be equal?
  3. The velocity v(cm/s) of a particle is given in terms of time t(in seconds) by the equation v = at+b/t+c. Dimension of a,b, and c are ?

Relative velocity in free fall

If a person jumps out of a plane, and a few seconds later, another person jumps, why is it that the difference in their velocities stays the same? Shouldn’t it decrease because eventually, the first diver will reach maximum velocity, but the other diver will be slower at first, but then he reaches max. velocity as well…I’m not wording it the best way, but any help would be greatly appreciated :]

[Posted by Iris]

Both are examples for free fall. The velocity at any instant is given by v = gt

If for the first one, time = t and for the second who jumps after n seconds, time=t-n

Therefore, velocity of the first one at any instant, v1=gt

for second one, v2=g(t-n)

The difference in velocities,

v1-v2 = gn, which shows that the difference in velocity remains constant.

This is because, both are moving with the same acceleration and their velocities are increasing at the same rate

A Numerical from Kinematics

Advait Asks:

“A test projectile is fired horizontally into a viscous liquid with a velocity u.The retarding force is propotional to the square of the velocity, so that the acceleration becomes a=-k(v)^2 .v is the velocity at that point. Derive expressions for the distance D travelled in the liquid and corresponding time t required to reduce the velocity to u/2.
Neglect any vertical  motion”

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