First slide

Projection Under uniform Acceleration

Question

Two identical projectiles are fired simultaneously as shown from the ground with the same magnitude of velocity and at the same angle with respect to the horizontal. The two projectiles collide at the highest point ‘B’ and coalesce. After how much time of firing them, they reach the ground ?

Moderate

A

usin/g
B

ucosα/g
C

2usinα/g
D

2ucosα/g

Solution

Conserving momentum at the highest point B, (m + m)v =m x ucosα + m(-ucosα) ⇒ v = 0
T = Time of flight of each projectile = 2usinα/g.
t = Time of free fall of the combined man = $\large \sqrt{\frac {2H_{max}}{g}}=\sqrt{\frac {u^2sin^2\alpha}{g^2}}=\frac {usin\alpha}{g}$
$\large \therefore Total\;time=\frac T2+t=\frac {usin\alpha}{g}+\frac {usin\alpha}{g}=\frac {2usin\alpha}{g}$

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