Problem 7: During a baseball game, a baseball is struck at ground level by a batter. The ball leaves the baseball bat with an initial speed v0 = 36 m/s at an angle θ = 18° above horizontal. Let the origin of the Cartesian coordinate system be the ball's position the instant it leaves the bat. Air resistance may be ignored throughout this problem. a) Express the magnitude of the ball’s initial horizontal velocity v0x in terms of v0 and θ. b) Express the magnitude of the ball’s initial vertical velocity v0y in terms of v0 and θ. c) Find the ball’s maximum vertical height hmax in meters above the ground.
Problem 7: During a baseball game, a baseball is struck at ground level by a batter. The ball leaves the baseball bat with an initial speed v0 = 36 m/s at an angle θ = 18° above horizontal. Let the origin of the Cartesian coordinate system be the ball's position the instant it leaves the bat. Air resistance may be ignored throughout this problem.
a) Express the magnitude of the ball’s initial horizontal velocity v0x in terms of v0 and θ.
b) Express the magnitude of the ball’s initial vertical velocity v0y in terms of v0 and θ.
c) Find the ball’s maximum vertical height hmax in meters above the ground.
d) Enter an expression in terms of v0, θ, and g for the time tmax it takes the ball to travel to its maximum vertical height.
e) Calculate the horizontal distance xmax in meters that the ball has traveled when it returns to ground level.
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