Final answer:
To find the initial speed of the ball, we can use the horizontal and vertical components of the initial velocity. To determine the time it takes for the ball to reach the wall, we can use the horizontal component of the velocity and the distance to the wall. Finally, to find the components of the velocity and speed of the ball when it reaches the wall, we can use the horizontal and vertical components of the velocity and the speed equation.
Step-by-step explanation:
To solve this problem, we can break it down into three parts: (a) finding the initial speed of the ball, (b) determining the time it takes for the ball to reach the wall, and (c) finding the components of the velocity and the speed of the ball when it reaches the wall.
(a) To find the initial speed of the ball, we can use the horizontal and vertical components of the initial velocity. We can use the equation:
V0x = V0 * cos(θ)
V0y = V0 * sin(θ)
where V0x and V0y are the horizontal and vertical components of the initial velocity, V0 is the initial speed of the ball, and θ is the angle of launch (35°). We can rearrange the equation for V0 to find:
V0 = √(V0x² + V0y²)
(b) To find the time it takes for the ball to reach the wall, we can use the horizontal component of the velocity and the distance to the wall. We can use the equation:
t = d / V0x
where t is the time, d is the distance to the wall, and V0x is the horizontal component of the initial velocity.
(c) To find the components of the velocity and speed of the ball when it reaches the wall, we can use the equations:
Vx = V0x
Vy = V0y - g * t
V = √(Vx² + Vy²)
where Vx and Vy are the horizontal and vertical components of the velocity, g is the acceleration due to gravity (9.8 m/s²), t is the time, and V is the speed of the ball.