# 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.

Question

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.

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Step 1

The expression for the velocity is,

Step 2

Here, the vector v is the velocity of the ball, vx is the horizontal velocity, vy is the vertical velocity, u is the initial velocity, θ is the angle of projection.

The expression for time taken for the ball to land is,

Step 3

Here, t is the time taken for the ball to land and s is the horizontal range of the ball.

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