How Much Farther Will Wonder Boy Hit the Baseball?

[muirp]

1. You have recently been struggling when stepping up to the plate to bat. You can no longer hit for power. To combat the problem you go see Bobby the bat boy and ask him for "Wonder Boy." This bat is 1.5 inch longer than the bat you currently use.
Assume that:
-you can swing both bats with an angular velocity of 2200 degree/s.
-including your arms and the length of your old bat--the radius of your swing 130 cm (to the contact point on the bat).
-your bat makes contact with the ball 1.2 m above the ground.

How much farther will you be able to hit a pitch with "Wonder Boy" which leaves your bat at an angle of 45 degrees if you measure the distance to the point where it lands on the ground?2. ANGULAR VELOCITY: change in theta/change in time, ARCLENTH: Theta(radius), Vt=angular velocity(r), At=(angular acceleration)(radius), Ac=(angular velocity^2)(radius) or Vt^2/radius.
3. I computed the velocity of the ball leaving the bat: Vt=angular velocity*radius=(2200degree/s*1.3m)=2860 m*degree/s. However, I just do not know where to go from here. Help please!

 

[BigJDubs]

Solution: To solve this problem, we need to apply the equation for projectile motion. The equation for projectile motion is given by:x = Vt x t x cos(θ)y = Vt x t x sin(θ) - (1/2) x g x t^2where Vt is the initial velocity of the ball, t is the time taken for the ball to reach the ground, θ is the angle of projection, and g is the gravitational acceleration. Since we know the initial velocity (Vt), the angle of projection (θ), and the gravitational acceleration (g), we can solve for the time taken for the ball to reach the ground. To do this, we can rearrange the equation for y and solve for t: t = (2 x y)/(Vt x sin(θ) - g)Substituting in the values given, we get: t = (2 x 1.2 m)/(2860 m*degree/s x sin(45 degrees) - 9.81 m/s^2)t = 0.0016582 s Now that we have the time taken for the ball to reach the ground, we can use the equation for x to determine the distance it will travel before hitting the ground. Substituting in the values given, we get: x = 2860 m*degree/s x 0.0016582 s x cos(45 degrees)x = 2.06 m Therefore, the ball will travel 2.06 m before hitting the ground when using the Wonder Boy bat.