According to the Guinness Book of World Records, the longest home run ever measured was hit by Roy "Dizzy" Carlyle in a minor-league game. The ball traveled 188 m (618 ft ) before landing on the ground outside the ballpark. Assuming that the ball's initial velocity was 45∘ above the horizontal, and ignoring air resistance, what did the initial speed of the ball need to be to produce such a home run if the ball was hit at a point 1.0 m (3.3 ft ) above ground level? Assume that the ground was perfectly flat.

A baseball slugger hits a pitch and watches the ball fly into the bleachers for a home run, landing h=6.5mℎ=6.5m higher than it was struck. When visiting with the fan that caught the ball, he learned the ball was moving with final velocity vf=31.35m/s at an angle θf=25.5∘ below the horizontal when caught. Assume the ball encountered no air resistance, and use a Cartesian coordinate system with the origin located at the ball's initial position. Create an expression for the ball’s initial horizontal velocity, v0,x, in terms of the variables given in the problem statement. Calculate the magnitude, in meters per second, of the vertical component of the ball’s initial velocity. Calculate the magnitude, in meters per second, of the ball’s initial velocity. Find the angle above the horizontal, in degrees, at which the ball left the bat.

Danielle launches a ball off of a platform of height h with velocity vo at an angle 0 above the horizontal. A wall with a ball-sized hole a height H above the floor, with H > h, is a horizontal distance L = 24.0 m away from Danielle. The difference in height between H and h is one-twelfth of L, and the square of the magnitude of the velocity, v, is three-halves of the product gL. H 1 H – h = h 3 L Determine the two values of 0 that ensure the ball passes through the hole. Submit the larger angle as 0, and the smaller angle as 02.

Consider a projectile launched with an initial velocity of 25.2m/s at an angle of θ0=30.9∘ above horizontal from level ground. After traveling a horizontal distance d=37.1m, it strikes a high cliff at a height hh above the original launch height. The impact angle, θ, may be above or below horizontal, depending upon whether or not the projectile has passed the apex of its flight. Use the Cartesian coordinate system provided in the drawing with the origin at the initial position of the projectile. Assume that air resistance is negligible.  Part (a)  How much time elapses, in seconds, from the moment the projectile is launched until it strikes the cliff?   Part (b)  At what height above the initial position, in meters, does the projectile strike the cliff?   Part (c)  What is the speed of the projectile, in meters per second, as it strikes the cliff?   Part (d)  What is the impact angle, in degrees measured counterclockwise from positive xxx, at which the projectile strikes the cliff?…