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Question

A particle is projected at angle θ with horizontal with velocity V0

Find

(i) tangential and normal acceleration of the particle at t = 0 and at highest point of its trajectory.

(ii) radius of curvature at t = 0 and highest point.



Correct Answer
A

at

Correct Answer
B

At highest point

Correct Answer
C

at

Correct Answer
D

At highest point


Solution

The correct options are
A

at


B

At highest point


C

at


D

At highest point


(i) The direction of tangential acceleration is in the line of velocity and the normal acceleration is in the direction perpendicular to velocity direction. The tangential and normal directions at O & P are shown in figure.
The net acceleration of the particle during motion is acceleration due to gravity i.e., 'g' is acting vertically downward.


At O:(at t=0)
Tangential acceleration at=-gsinθ
Normal acceleration an= gcosθ
At P (at highest point)
Tangential acceleration
at=0 an=g
(ii)  Let radius of curvature at O be R0. The normal acceleration at O is g cos θ.
an=v2RR0=v20an=v20gcosθ

Radius of curvature at P
Normal acceleration at P is 'g'
Rp=v2an=(v0cosθ)2g=v20cos2θg

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