(Solved): (a) A soccer player kicks a rock horizontally off a \( 48 \mathrm{~m} \) high ...

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(a) A soccer player kicks a rock horizontally off a \( 48 \mathrm{~m} \) high cliff into a pool of water. If the player hears the sound of the splash \( 3.29 \mathrm{~s} \) later, what was the initial speed given to the rock (in \( \mathrm{m} / \mathrm{s} \) )? Assume the speed of sound in air is \( 343 \mathrm{~m} / \mathrm{s} \). \[ x \] The time given in the problem can be divided into two intervals: the time for the rock to hit the water and the time for the sound to return to the kicker. \( \mathrm{m} / \mathrm{s} \) (b) What If? If the temperature near the cliff suddenly falls to \( 0^{\circ} \mathrm{C} \), reducing the speed of sound to \( 331 \mathrm{~m} / \mathrm{s} \), what would the initial speed of the rock have to be (in \( \mathrm{m} / \mathrm{s} \) ) for the soccer player to hear the sound of the splash \( 3.29 \mathrm{~s} \) after kicking the rock? \[ \mathrm{m} / \mathrm{s} \]