Step 1: Given information
From the figure,
![](https://uc1426683001f5670c298fa32111.previews.dropboxusercontent.com/p/thumb/ABk6_8hNKeqBQyaMZ3biAW-ZZKIXAZsaP6BkhGbd-nFslLdyVp3n0S1w0lqTTYM4j7uVTXgaOE7lHjYlO2y4u9ccwixWRhUloOHBlKwSnPl-D6xJtFpCU3kmkHW_xqjBIbPozfGUmJl20sq7x3tU_39I1q5Yw1vOhxTtmrDXz7pxBeQP6SGK5_UB42VTF_FIK5eBU3UPVDmzarnEHRmGV02EUAmBIDaoRbRxYwjzd9cGtxVNDvi4_yc19WDOS4x9KtjaZ4bPfgd32eZ7szY5H09yMaLUahMyV7hhuduwV0qgk_e2PZZSrnr6b-qdC1enKbfKR99A5thXadOg7Zpt1vLcxqITceYF0kKypzlhZvTpZpT8nIXlbgGqoe_IA8iWdK4/p.jpeg)
- We have to find out the radius of curvature of a projectile at point .
- It is already given that the projectile is fired with a velocity , making an angle with the horizontal.
- At this point, the projectile has an acceleration , which is the acceleration due to gravity.
Step 2: Formula for calculating the radius of curvature:
- The radius of curvature of a path at a point in a circle tells us how much the curve is at that point.
- The less the radius of curvature, the more pointed the curve .
- If the radius of curvature is infinite then it means that the curve is a straight line.
- Here we have to calculate the radius of curvature (R) for a projectile at its highest point from the ground.
- At the highest point, the vertical component of velocity of the projectile is and it has velocity only along with the horizontal direction i.e. .
The relation between acceleration,(centripetal acceleration), radius, and velocity of the body in a uniform circular motion can be given by:
Where, is acceleration due to gravity
Step 3: Calculating the radius of curvature
By Substitute the given value of velocity, in the given equation, we get
The radius of curvature at point ,
Hence this is the required radius of curvature of a projectile at point .