physics kinematics problem?

Question

hello i am working on homework for physics since and i came across a question that i cannot solve! if you guys/girls could show me how to solve the following question i will greatly appreciate it

here it is:

a passenger in a hot-air balloon throws a ball with an unknown Vi. The ball accelerates at 9.8 m/s^2 [down] for 2 seconds, at which time its instantaneous velocity is 24 m/s[45 degrees below the horizontal]. Determine the ball's Vi.

the answer in the back of the book is: 17 m/s[10 degrees above the horizontal]

thanks a lot for any help

Answer 1

Break the velocity into horizontal and vertical components.

Vf_x = (24m/s)cos45
Vf_y = (-24m/s)sin45

The x-component of velocity doesn't change: so:
Vf_x = Vi_x = (24m/s)cos45

The y-component of velocity changes by 9.8m/s every second, so:
Vf_x = Vi_x – g(2sec)

or:
Vi_x = Vf_x + g(2sec)
= (-24m/s)sin45 + (9.8m/s²)(2sec)

Now you know Vi_x and Vi_y, so you can use:

Vi = sqrt((Vi_x)² + (Vi_y)²)

and:

Tanθ = Vi_y / Vi_x