Basketball game problem- projectile motion

[mmoadi]

Homework Statement

Basketball player throws the ball form the middle of the court one second before the game ends. How much must the initial speed of the ball be and at what angle it must be thrown, if it should hit the basket at the exact time of siren without preceding reflection from board? Length of playground is 26 m, the distance between the floor and the ring is 306 cm, and the ball is thrown from height 206 cm. Neglect the rotation of the ball. At what angle and with what velocity (speed) the ball hits the basket?

Homework Equations

Δx= v0xt
Δy= v0yt – ½(gt²)
v0= sqrt(v0x² + v0y²)
tan α= v0y / v0x

The Attempt at a Solution

What I know:
t= 1 s
L= 26 m
Δx= 13 m
h1= 206 cm
h2= 306 cm
Δy= 100 cm = 1 m

What I’m looking for:
v0= ? m/s (initial velocity)
α = ? ° (launch angle)
vf= ? m/s (final velocity)
β= ? ° (impact angle)

① First, I calculated the v0x = vx: v0x= Δx / t = 13 m/s
② Second, I calculated v0y: v0y= (2Δy + gt²) / 2t= 5.4 m/s
③ I know calculated v0 from the Pythagoras formula: v0= sqrt(v0x² + v0y²)= 14.08 m/s
④ And know I calculated the launching angle α: α= (tan)-¹(v0y / v0x)= 22.56°

What is left know are final velocity and impact angle. Can I just state that final velocity = initial velocity (conservation of energy) and that impact angle = launch angle (symmetry of parabola)? Or, do I have to do new calculations because the basketball ring is higher than the launching height of the ball and the parabola is not symmetrical? If second is the case, I really need help, because I don’t know how to approach it now.

Thank you for helping!

 

[willem2]

You can't say that final velocity = initial velocity (conservation of energy), because
you have to account for the increase in potential energy of the ball.

another option is to use V_f = V_i + a t and compute a new v_x and v_y