Question 1

A ball is thrown from the location (x_0, y_0 )=(0,0) of a horizontal playground with an initial speed v_0 at an angle _0 from the +x-direction. The ball is to be hit by a stone, which is thrown at the

Accepted Answer

For case I : a_ rel =0 For collision v _0 2 = v 2 v = v _0 So T _1= L v _0 2 + v 2 _1= L 2 v _0 . .(1) For case II, a_ rel =0 For collision, v _0 3 2 = v 2 aligned & v = 3 v _0 \ & So, T _2= L v _0 2 + v 3 2 \ & ~T _2= L v _0 2 + 3 v _0 2 \ & T _2= L 2 v _0 . .(2) \ & so, ( T _1 ~T _2 )^2=( 2 )^2=2 ( T _1 ~T _2 )^2=2 aligned

Question 2

Starting at time  t = 0 from the origin with speed  1 &#160; m &#160; s - 1 , a particle follows a two-dimensional trajectory in the  x - y plane so that its coordinates are related by

Accepted Answer

y = x 2 2 d y d t = 1 2 × 2 x d x d t v y = x v x d v y d t = d x d t × d x d t + x d 2 v x d t 2 a y = v x 2 + x a x If x = 0 , a y = v x 2 = 1 , No matters what is the value of a x hence, Option A is correct. If a x = 0 then x = v x t = t at t = 1 ; x = 1 m then angle made by velocity vector with x -axis tan θ = v y v x = x = 1 ⇒ θ = 45 °

Motion In One Dimension — Previous Year Questions & Solutions