Question

The speed of a projectile at its maximum height is half of its initial speed

Answer 1

Answer:

What is the angle of projection if the speed of a projectile when it is at the greatest height is the root of 2/5 times its speed at half of the maximum height? A projectile is launched at an angle of 35 degrees from the horizontal and lands 20 seconds later at the same height as it was launched.

Answer 2

At maximum height, only horizontal velocity exists. Thus,

$\displaystyle\longrightarrow\sf{u\cos\theta=\dfrac{u}{2}}$

$\displaystyle\longrightarrow\sf{\cos\theta=\dfrac{1}{2}}$

$\displaystyle\longrightarrow\sf{\underline{\underline{\theta=60^o}}}$

Then, horizontal range,

$\displaystyle\longrightarrow\sf{R=\dfrac{u^2\sin(2\theta)}{g}}$

$\displaystyle\longrightarrow\sf{R=\dfrac{u^2\sin120^o}{g}}$

$\displaystyle\longrightarrow\sf{\underline{\underline{R=\dfrac{u^2\sqrt3}{2g}}}}$