Question

A batted baseball leaves the bat at an angle of 33.0° above the horizontal and is caught by an outfielder 395 ft from home plate at the same height from which it left the bat. What is the initial velocity of the baseball?

Answer 1

To find the initial velocity of the baseball, we can use the equations of projectile motion and the given values of the angle and horizontal distance.

Step-by-step explanation:

To find the initial velocity of the baseball, we can use the equations of projectile motion. The horizontal component of the initial velocity remains constant throughout the motion, while the vertical component changes due to the acceleration due to gravity. We can use the horizontal and vertical components to calculate the initial velocity.

Given that the baseball is caught at the same height it left the bat, we can assume that the time of flight is the same for the upward and downward motion. Using this information, we can find the time of flight by dividing the total horizontal distance by the horizontal component of the initial velocity.

Once we have the time of flight, we can use it to calculate the vertical component of the initial velocity. We know that the vertical displacement is zero, so we can use the equation for vertical displacement in projectile motion to find the initial vertical velocity. Finally, we can use the horizontal and vertical components to find the magnitude of the initial velocity using the Pythagorean theorem.

Using the given values of the angle of 33.0° and the horizontal distance of 395 ft, we can substitute these values into the equations and calculate the initial velocity of the baseball.