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84 PHYSICS

v ( sinq o ) 2
h m = o
2g
The time taken to reach this height is :

o
t m = v sin θ o
g
The horizontal distance travelled by a projectile from its initial position to the position
it passes y = 0 during its fall is called the range, R of the projectile. It is :
v 2
R = o sin2θ
g o
17. When an object follows a circular path at constant speed, the motion of the object is
called uniform circular motion. The magnitude of its acceleration is a = v /R. The
2
c
direction of a is always towards the centre of the circle.
c
The angular speed ω, is the rate of change of angular distance. It is related to velocity
2
v by v = ω R. The acceleration is a = ω R.
c
If T is the time period of revolution of the object in circular motion and ν is its
2 2
frequency, we have ω = 2π ν, v = 2πνR, a = 4π ν R
c

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