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A batter hits a pitched ball when the center of the ball is 1.22 m above the ground. The ball leaves the bat at an angle of 45° with the ground. With that launch, the ball should have a horizontal range (returning to the launch level) of 107 m.
A batter hits a pitched ball when the center of the ball is 1.22 m above the ground. The ball leaves the bat at an angle of 45° with the ground. With that launch, the ball should have a horizontal range (returning to the launch level) of 107 m. (a) Does the ball clear a 7.32-m-high fence that is 97.5 m horizontally from the launch point?
(b) At the fence, what is the distance between the fence top and the ball center?
Answer:2.56mExplanation:This is problem 4.47 from your textbook.Find: Whether a batted baseball clears a fence, and by what amount it does or does not.Given: The baseball’s initial launch height and angle, the range the baseball would have without the fence, the distance to the fence and its height.Let the y axis run vertically and the x axis horizontally. Let the range the baseball would have without the fence be R=107 m, with the distance to the fence d=97.5m and its height hfence=7.32 m. The baseball is batted at an angle θ=45° at speed vi a height of hbat=1.22m above the ground.Let the origin be at the position the ball leaves the bat. The height of the fence relative to the height of the bat is thenδh = hfence − hbatWhat we really need to determine is the ball’s y coordinate at x = d. If y > δh, the ball clears the fence. We can use the range the baseball would have without the fence and the launch angle to find the ball’s speed, which will allow a complete calculation of the trajectory.Relevant equations: We need only the equations for the range and trajectory of a projectile over level ground:R = (vi*sin2θ)/gFor convenience sake and easy reading, I extracted the solution of your textbook for the remaining parts of the solution.Hence, it is seen that the ball does clear the fence, by approximately 2.56 m...