A boy's hand pushes a ball through a vertical distance of 1.45 m as he throws the ball straight upward. Once the ball leaves his hand it travels an additional 22 m (straight up) before returning to earth. Find the acceleration of the ball while it was in the boy's hand
You need to find the vertical velocity of the ball at launch.
The PE at the top=KE at launch
mg*22=1/2 m v^2
v= sqrt (2*g*22) m/s
now, considering just the period throwing
vf^2=vi^2+2ad
vf=above
vi=0
d=1.45m
solve for a
To find the acceleration of the ball while it was in the boy's hand, we need to use the equations of motion.
The relevant equation of motion is:
s = ut + (1/2) * at^2
Where:
s is the vertical distance traveled (1.45m)
u is the initial velocity (which is 0 since the ball starts from rest in the boy's hand)
a is the acceleration
t is the time taken to cover the distance (which we need to find)
Since the initial velocity is 0, we can simplify the equation to:
s = (1/2) * at^2
Plugging in the given values:
1.45 = (1/2) * a * t^2
To solve for a, we need to find the value of t. We can do this by using the equation of motion:
v = u + at
Where:
v is the final velocity (which is 0 when the ball returns to earth)
u is the initial velocity (which is 0 since the ball starts from rest in the boy's hand)
a is the acceleration
t is the time taken to reach the final velocity (which we need to find)
Since the initial and final velocities are both 0, we can simplify the equation to:
0 = 0 + a * t
This tells us that a * t = 0, which means that either a = 0 or t = 0.
Since we know that the ball is thrown upward by the boy, we can assume that the acceleration is not zero. Therefore, we conclude that t = 0.
Now, plugging t = 0 into the first equation:
1.45 = (1/2) * a * 0^2
1.45 = 0
This is not possible because the left side is a non-zero value. Therefore, it implies that the initial assumption of the boy's hand being responsible for the 1.45m distance is incorrect.
Hence, we cannot determine the acceleration of the ball while it was in the boy's hand based on the given information.