First slide

Projection Under uniform Acceleration

Question

A projectile A is projected from ground. An observer B running on ground with uniform velocity of magnitude 'v' obseryes A to move along a straight line. The time of flight of A as measured by B is T. Then the range R of projectile on ground is

Moderate

A

R = vT
B

R < vT
C

R > vT
D

Information insufficient to draw inference

Solution

The horizontal and vertical components of initial velocity of projectile are as shown in figure. Since the observer moving with uniform velocity v sees the projectile moving in straight line
Hence v = u $cosθ$
The time of flight as measured by observer B T = $\frac{2 u \sin θ}{g}$
Hence horizontal range of projectile on ground
R = ( $u \cos θ$ )T = vT

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