Question

If a baseball is batted at an angle of 35° to


the ground, the distance the ball travels


can be estimated using the equation


d = 0. 0034s2 + 0. 004s – 0. 3, where s is the


bat speed, in kilometres per hour, and d is


the distance flown, in metres. At what speed


does the batter need to hit the ball in order


to have a home run where the ball-flies


125 m? Round to the nearest tenth.

Answer 1

The speed the batter needs to hit the ball to have a home run where the ball flies 125 m is 191.4 km/h.

We have distance flown, in meters, d = 0.0034s² + 0.004s - 0.3

where s is the bat's speed, in kilometers per hour.

We need to find s when d = 125 m.

Substituting the values,

d = 0.0034s² + 0.004s - 0.3

125 = 0.0034s² + 0.004s - 0.3

0.0034s² + 0.004s - 125.3 = 0

s = 191.38 km/h    or   s = -192.56 km/h ( Not possible)

The batter needs to hit the ball at a speed of 191.4 km/h

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