Question

A projectile is thrown into the air at an angle. What is its velocity when the projectile reaches its maximum height?

is it correct that it's equal to the horizontal and vertical component of its initial velocity? please explain why too.

Answer 1

It is equal to the horizontal component of the initial velocity. Reason is that acceleration due to gravity is acting downwards which changes only the vertical component of the velocity. So, during the projectile motion , vertical component keeps on changing while the horizontal component remains same throughout the trajectory(Assumption: we neglect air friction). At the maximum height, vertical motion is zero which means upward component of velocity has been completely balanced out by the downward force exerted by gravity. So, the only component of velocity left at max height is the 'horizontal component of the initial velocity'.

Answer 2

in simple word.................
the velocity at highest point will be equal to the horizontal component of the initial velocity.
this is because at the highest point the vertical component of velocity will be zero.as horizontal velocity is constant ,velocity at highest point is equal to the horizontal velocity