A projectile takes time T₁ between points A and D at the same vertical height and T₂ between higher equal-height points B and C, separated vertically by h. If h=(g/x)(T₁²−T₂²), find x.
Physics · Mixed Chapter
JEE Main Practice

Question

A projectile takes time T₁ between points A and D at the same vertical height and T₂ between higher equal-height points B and C, separated vertically by h. If h=(g/x)(T₁²−T₂²), find x.

G1 Physics · Accepted Answer

Step 1: For any horizontal level at height y, the two crossing times have separation T(y)=2√(uᵧ²−2gy)/g. Step 2: Thus T₁²=4uᵧ²/g² for base level A–D. Step 3: At higher level B–C, T₂²=4(uᵧ²−2gh)/g². Step 4: Subtract: T₁²−T₂²=(8h/g). Rearranged h=g(T₁²−T₂²)/8, so x=8.