Question

Take the z-axis as vertical and the xy plane as horizontal. A particle A is projected at 4Ö2 m/s at an angle of 45⁰ to the horizontal, in the xz plane. Particle B is projected at 5 m/s at an angle q = tan^–1(4/3) to the y-axis, in the yz plane. Which of the following is not correct for the velocity of B with respect to A?

• A. Its initial magnitude is 5 m/s.
• B. Its magnitude will change with time.
• C. It lies in the xy plane
• D. It will initially make an angle (q + p/2) with the positive x-axis

Answer 1

Answer: (B)

Its magnitude will change with time.

Answer 2

$\overrightarrow { \mathrm { v } } _ { \mathrm { A } } = 4 \sqrt { 2 }$ cos 45º $\hat { \mathbf { i } }$ + $4 \sqrt { 2 }$ sin $45 ^ { \circ } \hat { j }$ ̃ $\overrightarrow { \mathrm { v } } _ { \mathrm { A } } = 4 \hat { \mathrm { i } } + 4 \hat { \mathrm { k } }$

$\overrightarrow { \mathrm { v } } _ { \mathrm { B } } = 5 \cos \theta \hat { \mathrm { j } } + 5 \sin \theta \hat { \mathrm { k } }$ = $3 \hat { j } + 4 \hat { k }$

$\overrightarrow { \mathrm { v } } _ { \mathrm { B } / \mathrm { A } } = \overrightarrow { \mathrm { v } } _ { \mathrm { B } } - \overrightarrow { \mathrm { v } } _ { \mathrm { A } } = 3 \hat { \mathrm { j } } - 4 \hat { \mathrm { i } }$ , $\overrightarrow { \mathrm { a } } _ { \mathrm { B } / \mathrm { A } } = \overrightarrow { \mathrm { a } } _ { \mathrm { B } } - \overrightarrow { \mathrm { a } } _ { \mathrm { A } }$

= – $g \hat { k } - ( - g \hat { k } ) = 0$