You throw a ball. The ball leaves your hand with a velocity of 15 m/s at an angle 60 degrees above the horizontal. Acceleration due to gravity is 9.8 m/s/s.
a) Determine the velocity (magnitude and direction) of the ball at the maximum height.
b) How much time does it take for the ball to reach maximum height?
c) Determine the maximum height.
(I know how to draw the diagram, so that part is good)
I think the components of the velocity at maximum height can be found using these equations:
a) VoY= Vosin60 = 15m/s(sin60) = 12.99 m/s velocity of ball in vertical direction (initial)
VoX= Vocos60 = 15 m/s(sin60) = 7.5 m/s velocity of ball in horizontal direction (initial)
Since there is no vertical velocity at max height, then the velocity at max height is just the magnitude of the horizontal component: 7.5 m/s horizontal direction??????
b) Time = Vy= VoY + ayt , set Vy = 0 at Y max.
0 = 12 m/s + (-9.8 m/s/s)t
t = (Vfy - Voy)/ -9.8m/s/s = (0 - 12.99)/-9.8 m/s/s = 1.32 seconds
c) Ymax. = Voyt + 1/2at^2 = (12.99 m/s)(1.32 sec.) + 1/2(-9.8m/s/s)(1.32 sec.)^2
= 8.60 meters max height
The Attempt at a Solution
see above. im not sure if i did this problem correctly, or if i understand it quite. there are some things about it that i understand, others not so much.
I think the velocity at max height would just be the component 7.5 m/s in the horizontal direction, since suposedly, there is no vertical velocity at max height. Is this assumption correct? Have i used the correct equations and in the right context?? If not, please help me to understand this type of problem better.
I understand that at max height, there is only the force of gravity 9.8 m/s/s downward, the horizontal velocity for a projectile is constant, and there is no horizontal acceleration. I assume there is no horizontal acceleration, because the horizontal veloc. remains constant?
However, if there is no vertical velocity at max height then why is the object still accelerating at 9.8 m/s/s downward due to gravity??? It seems like a contradiction, something cant be accelerating due to some force and not also have a velocity. Increasing velocity is the definition of acceleration, so there would be vertical velocity at max height. There is always vertical velocity due to the force of gravity accelerating the object downward.