Question

For a flourish at the end of her act, a juggler tosses a single ball high in the air. She catches the ball 3.3 s later at the same height from which it was thrown.

Part A What was the initial upward speed of the ball?
Express your answer to two significant figures and include appropriate units.

Answer 1

The initial upward speed of the ball is approximately 16 m/s, calculated using the formulas for uniformly accelerated motion considering the time to reach the peak and the acceleration due to gravity.

Step-by-step explanation:

The initial upward speed of the ball can be calculated using the formulas for uniformly accelerated motion, where gravity is the only acceleration acting on the ball. Since the ball takes 3.3 seconds to return to the same height, we can divide this time in half to find the time it takes to reach the peak of its flight, which will be 1.65 seconds. Assuming gravity (g) to be -9.81 m/s2 (negative because it's directed downward), we can use the formula v = u + at, where v is the final velocity (0 m/s at the peak), u is the initial upward speed we need to find, a is the acceleration due to gravity, and t is the time to reach the peak. Solving for u gives us:

0 = u + (-9.81 m/s2)(1.65 s)

u = (9.81 m/s2)(1.65 s)

u = 16.19 m/s

Therefore, the initial upward speed of the ball is approximately 16 m/s, rounded to two significant figures.

Answer 2

Initial speed of the ball, u = 16 m/s

Step-by-step explanation:

It is given that, a juggler tosses a single ball high in the air. She catches the ball 3.3 s later at the same height from which it was thrown. Let u is the initial upward speed of the ball.

At the highest point, the final speed of the ball, v = 0

Using equation of motion as :

`v=u+at`

a = -g

`0=u-gt`

Let
`t_a\ and\ t_d` are time of ascent and descent respectively.

So, total time,
`t=(2u)/(g)`

`3.3=(2u)/(9.8)`

u = 16.17 m/s

or

u = 16 m/s

So, the initial upward speed of the ball is 16 m/s. Hence, this is the required solution.