Final answer:
To determine the trajectory of Frank Thomas's hit baseball, projectile motion equations must be used to calculate the height of the ball when it reaches the wall, the time in the air, the total range, the maximum height, and the distance the ball would travel if it left the bat at a 31° angle.
Step-by-step explanation:
To calculate the trajectory of the baseball hit by Frank Thomas, we'll use the kinematic equations for projectile motion. Assuming no air resistance, and taking the acceleration due to gravity to be 9.8 m/s2, we start by resolving the initial velocity into horizontal (vx) and vertical (vy) components:
- vx = v * cos(θ)
- vy = v * sin(θ)
Here, v is the initial velocity (40 m/s) and θ is the launch angle (we'll use 29 degrees, converting to radians for calculations). To find out whether it is a home run:
- Calculate the time t it takes for the ball to reach the wall, using the horizontal component and the distance to the wall.
- Use this time to calculate the height h of the ball when it reaches the wall.
- If this height is greater than the wall height, it's a home run.
To find the time the ball is in the air, we use the vertical motion and solve for t when the vertical displacement is 0 (since it's 1 meter above the ground when hit).
The range c) and the maximum height d) can also be found using the kinematic equations for projectile motion..
If the ball was hit at a 31° angle instead, the same process but with a different angle is used to find the new range.