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A ball player hits a home run, and the baseball just clears a wall 17.3 m high located 129.0 m from home plate. The ball is hit at an angle of 35° to the horizontal, and air resistance is negligible. Assume the ball is hit at a height of 1.0 m above the ground.

(a) What is the initial speed of the ball in m/s?
(b) How much time does it take for the ball to reach the wall in seconds?
(c) Find the components of the velocity and the speed of the ball when it reaches the wall.

User Friism
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1 Answer

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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.

User Josua M C
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