Projectile Motion Ball Drop: Solving for Initial Velocity with Given Angles

[Oblivion77]

Homework Statement

A Ball is dropped onto a step at point A and rebounds with a velocity Vo at an angle 15 degrees with the vertical. Determine the value of V₀ knowing that just before the ball bounces at Point B its velocity V_B forms an angle of 12 degrees with the vertical.

Homework Equations

X = Vt
Y = Vt - 0.5gt²

The Attempt at a Solution

X = (VoSin15)t
Y = (VoCos15)t -0.5gt²

I am not sure how to make use of the other information provided.

 

[lewando]

The most relevant equation:

Vy(t)^2 = Vy0^2 + 2g (y(t) - y0)

because we need to use the 0.2m y-displacement.

Also noteworthy:
Vx0 = V0 sin(15)
VxT = VT sin(12)
Vx0 = VxT

 

[nlightner]

Can you please clarify?

Based on the given information, we can use the fact that the velocity of the ball at point A (before it bounces) is equal to the velocity of the ball at point B (after it bounces), since there is no external force acting on the ball. Therefore, we can set the equations for velocity in the x and y directions at point A equal to the equations for velocity in the x and y directions at point B. This gives us:

VoSin15 = VBsin12 (since the x velocity remains constant)
VoCos15 - gt = VBcos12 (since the y velocity decreases due to gravity)

From these two equations, we can solve for Vo by isolating it in one of the equations and substituting it into the other equation. This will give us a value for Vo that satisfies both equations. Once we have this value, we can plug it back into the original equations for x and y velocity (X and Y) to solve for the time it takes for the ball to reach point B (since we know the initial velocity and the angle, we can solve for t in the equations X = Vt and Y = Vt - 0.5gt2). Then, we can use the value of t to solve for the initial velocity using the equation Vo = X/t.