projectiles

a golf ball is struck at a point O on the ground and moves with an initial velocity of 20ms-1 at an angle of 53* to the horizontal. the ball subsequently lands at a point x which is on the same horizontal level as O.

for parts and b i worked out the time to reach point x is 3.26 and the distance between O and X is 39.2m

however i dont undestand part c
ci. state the least speed of the ball during its flight from 0 to X
cii. state the direction of motion of the ball when this least speed occurs

please explain, thanks!

c.i. The ball moves with some velocity which is changing. It has a vertical velocity component, and a horizontal velocity component. The horizontal one does not change at all and remains constant. Therefore, for the minimum speed, you want to identity what the minimum vertical component must be in that motion and use it in determining the magnitude of that velocity.

c.ii. Once you figure out WHEN precisely this minimum vertical velocity occurs (not in terms of time, but in terms of the motion) then it should be fairly obvious in what direction it is going.

i know the vertical component is 20sin53 and the horizontal component is 20cos53 but how do i work out the minimum vertical component.

Think about the projectile moving. It must go up and then it must come down. When does the minimum vertical speed occur?? What must it be?

when its at the highest point? im not sure

Of course! So what is the vertical speed at the highest point?

You don't even need to study Mechanics to know this, it's just intuitive.

zero?

zero too, i think

No, because we have the horizontal component which we know isn't zero.

You have a velocity where there's a known horizontal vel, and vertical vel is 0... so the magnitude of this velocity is...?

oh yes, so its cos53?

even thought velocity is 0 at that point?

(for the 100th time...) Vertical velocity is zero at that point. Not the horizontal one! The horizontal one is 20cos53 throughout!