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Standard XII

Physics

Oblique Collision

In the fig. s...

Question

In the fig. shown below a body is projected with velocity $u_{1}$ from the point A at the same time another body is projected vertically upwards with the velocity $u_{2}$ from the point B. What should be the value of $u_{1}$ / $u_{2}$ for both the bodies to collide.

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Solution

For projectile,
$u_{y} = u_{1} sin 60^{o} u_{x} = u_{1} cos 60^{o} F o r u_{2}, u_{y} = u_{2} T o c o l l i d e, t_{1} = t_{2}, H_{1} = H_{2} ∴ H = u t - \frac{1}{2} g t^{2} \frac{u_{1}}{u_{2}} = \frac{1}{sin 60^{o}} = \frac{2}{\sqrt{3}}$

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In the fig. shown below a body is projected with velocity u1 from the point A at the same time another body is projected vertically upwards with the velocity u2 from the point B. What should be the value of u1/u2 for both the bodies to collide.

For projectile,uy=u1sin60oux=u1cos60oForu2,uy=u2Tocollide,t1=t2,H1=H2∴H=ut−12gt2u1u2=1sin60o=2√3

In the fig. shown below a body is projected with velocity $u_{1}$ from the point A at the same time another body is projected vertically upwards with the velocity $u_{2}$ from the point B. What should be the value of $u_{1}$ / $u_{2}$ for both the bodies to collide.

For projectile,
$u_{y} = u_{1} sin 60^{o} u_{x} = u_{1} cos 60^{o} F o r u_{2}, u_{y} = u_{2} T o c o l l i d e, t_{1} = t_{2}, H_{1} = H_{2} ∴ H = u t - \frac{1}{2} g t^{2} \frac{u_{1}}{u_{2}} = \frac{1}{sin 60^{o}} = \frac{2}{\sqrt{3}}$