Question

a particle is projected in x -y plane with gravity along -y direction. its equation of motion is given by y=bx-cx2. find the range of the projectile

Answer 1

Answer:

The range of the projectile can be obtained by differentiating the equation with respect to x and equate it to zero

This is because the y(vertical height) will become zero after the range of the projectile is covered.

y= bx-cx2

dy/dx = b- 2cx = 0

b- 2cx=0

x= b/2c

So the range of the projectile is b/2c

Explanation:

Answer 2

Answer: range b/c

Explanation:

Differentiate both side with respect to time you will get dy/dt

And b-c2x now equate b-c2x=0 because at maximum height dy/dt will be zero.
here you will get x=b/2c now for half distance range double of this

So.  2* b/2c = b/c .

thankyou.