Question

The height h in feet of a baseball on Earth after t seconds can be modeled by the function h(t) = -16(t - 1.5)2 + 36, where -16 is a constant in ft/s2 due to Earth's gravity. The gravity on Mars is only 0.38 times that on Earth. If the same baseball were thrown on Mars, it would reach a maximum height 59 feet higher and 2.5 seconds later than on Earth. Write a height function for the baseball thrown on Mars.


A short stop makes an error by dropping the ball. As the ball drops, its height h in feet as a function of time, t, is modeled by h(t) = -16t2 + 3. A slow motion replay of the error shows the play at half speed. What function describes the height of the ball in the replay? (Hint: The function squares the time, so half the time is also squared in the new function.)


A baseball is thrown with a vertical velocity of 50 ft/s from an initial height of 6 ft. The height h in feet of the baseball can be modeled by h(t) = -16t2 + 50t + 6, where t is the time in seconds since the ball was thrown. It takes the ball approximately _____ seconds to reach its maximum height. (Round to the nearest tenth of a second and enter only the number.)


To the nearest foot, what is the maximum height that the ball reaches? (Enter only the number.)


A player hits a foul ball with an initial vertical velocity of 70 ft/s and an initial height of 5 feet. The maximum height reached by the ball is _____ feet. (Round to the nearest foot and enter only the number.)


A baseball player hits a ball toward the outfield. The height h of the ball in feet is modeled by h(t) = -16t2 + 22t + 3, where t is the time in seconds. In addition, the function d(t) = 85t models the horizontal distance d traveled by the ball. If no one catches the ball, how long will it stay in the air? (Round to the nearest tenth of a second and enter only the number.)


To the nearest tenth of a foot, what is the horizontal distance that the ball travels before it hits the ground? (Enter only the number.)


A pitch may result in a strike if its height is between 2.5 and 5 feet when it crosses home plate. This range is called the batter's strike zone. The pitcher throws the ball from a height of 6 feet with an initial vertical velocity of 5 ft/s and a horizontal velocity of 116 ft/s. Can this pitch result in a strike?


The height h in feet of a baseball hit from home plate can be modeled by the function h(t) = -16t2 + 32t + 5.5, where t is the time in seconds since the ball was hit. The ball is descending when it passes 7.5 feet over the head of a 6-foot player standing on the ground. To the nearest tenth of a second, how long after the ball is hit does it pass over the player's head? (Enter only the number rounded to the nearest tenth.)


The horizontal distance between the player and home plate is 120 ft. Use your answer from the previous question to determine the horizontal speed of the ball to the nearest foot per second.



An outfielder throws a baseball to the player on third base. The height h of the ball in feet is modeled by the function h(t) = -16t2 + 19t + 5, where t is time in seconds. The third baseman catches the ball when it is 4 feet above the ground. To the nearest tenth of a second, how long was the ball in the air before it was caught?



A player on the opposing team starts running from second base to third base 1.2 s before the outfielder throws the ball. The distance between the bases is 90 ft, and the runner's average speed is 27 ft/s. Will the runner reach third base before the ball does?

Answer 1

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