A juggler tosses a 0.4kg ball straight up at 8m/s, and then catches it at the same height .

a. determine the acceleration on the way up and down
b. determine the total amount of time spent in the air by the ball. (hint: you know the displacement)
c.determine the velocity of the ball just as the juggle catches it. (Hint: it is not zero)

where is the displacement ?

I was confused there too cause the problem didn't tell me the displacement so I don't know how to find acceleration.

I finally decided one was supposed to use -9.8m/s^2

a. g=9.8 m/s²

b. Upward:
v=v₀-gt
v=0 => t=v₀/g =8/9.8 =0.82 s.
t(up) =t(down)
t(total)=2•0.82=1.64 s.
c. v=v₀=8 m/s

To answer these questions, we can apply the laws of motion and kinematics. Let's break down each part:

a. To determine the acceleration on the way up and down, we need to find the acceleration during each phase separately. The acceleration when the ball is moving upwards will be opposite to the acceleration when it is moving downwards due to the gravitational force acting on the ball.

During the upward motion:
We can use the kinematic equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. In this case, the initial velocity u is 8 m/s, the final velocity v is 0 m/s (at the highest point), and the displacement s is unknown. The acceleration a can be calculated using the formula F = ma, where F is the gravitational force and m is the mass of the ball.

Since the ball is going straight up, the force due to gravity acting on the ball will be in the opposite direction to the motion. Therefore, the acceleration will be equal to -9.8 m/s^2 (taking the magnitude of acceleration and considering the direction).

During the downward motion:
The acceleration due to gravity acts in the same direction as the motion, so the acceleration will be +9.8 m/s^2.

b. To determine the total time the ball spends in the air, we can use the fact that the displacement is zero when the ball reaches its highest and lowest points during the motion. We can use the kinematic equation s = ut + (1/2)at^2, where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time.

Since the displacement is zero, the equation simplifies to 0 = ut + (1/2)at^2. Since we know the initial velocity and the acceleration during the upward and downward motion, we can solve this equation to find the total time spent in the air.

c. To determine the velocity of the ball when the juggler catches it, we need to consider the velocity at the same height where the ball was initially thrown (the apex of the ball's motion). At this point, the velocity will be in the opposite direction but will have the same magnitude as its initial velocity (8 m/s), as there is no horizontal force acting on it in this scenario.

So, to summarize:
a. The acceleration on the way up is -9.8 m/s^2 (opposite direction to motion), and the acceleration on the way down is +9.8 m/s^2 (same direction as motion).
b. The total time spent in the air can be found using the kinematic equation when displacement is zero.
c. The velocity of the ball when the juggler catches it is 8 m/s in the opposite direction to its initial velocity.