MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Finding Average Velocity

A particle is...

Question

A particle is projected with a velocity u making an angle $θ$ with the horizontal. What is the radius of curvature of the parabola where the particle makes an angle $θ$ /2 with the horizontal?

Open in App

Solution

$_{i n} = u c o s θ^i + u s i n θ^j a n d \to v (t) = u c o s θ^i + (u s i n θ - g t)^j a t t i m e t t h e a n g l e o f t h e p r o j e c t i l e i s θ / 2 \frac{u s i n θ - g t}{u c o s θ} = t a n θ / 2 \Rightarrow u s i n θ - g t = u c o s θ t a n θ / 2 \to v (t) = u c o s θ^i + (u c o s θ t a n θ / 2)^j \Rightarrow v = \sqrt{{(u c o s θ)}^{2} + {(u c o s θ t a n θ / 2)}^{2}} \Rightarrow v = u c o s θ s e c θ / 2 R = \frac{v^{2}}{g c o s θ / 2} = \frac{u^{2} {c o s}^{2} θ {s e c}^{2} θ / 2}{g c o s θ / 2} = \frac{u^{2} {c o s}^{2} θ}{g {c o s}^{3} θ / 2}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. A particle is projected with a speed u at an angle

θ

with the horizontal. What is the radius of curvature of the parabola traced out by the projectile at a point where the particle velocity makes an angle

\frac{θ}{2}

with the horizontal.

Q. A particle is projected with a speed

u

θ

with the horizontal. Find the radius of curvature of the parabola traced out by the projectile at a point, where the particle velocity makes an angle

θ / 2

with the horizontal.

Q. A particle is projected with a velocity u at an angle with the horizontal plane. Find the radius of curvature of the parabola traced out by the particle at the point where velocity makes an angle

\frac{θ}{2}

with the horizontal plane.

Q. What is the radius of curvature of the parabola traced out by the projectile projected at a speed

v

and projected at an angle

θ

with the horizontal at a point where the particle velocity makes an angle

\frac{θ}{2}

with the horizontal?

Q. What is the radius of curvature of the parabola traced by a projectile with initial speed

u

2 θ

with the horizontal, at a point where the velocity of the particle makes an angle

θ

with the horizontal?

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Speed and Velocity

PHYSICS

Watch in App

explore_more_icon

Explore more

Finding Average Velocity

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon