A ball is thrown up 90 feet in the air. it comes down, bounces, and then...
A ball is thrown up 90 feet in the air. it comes down, bounces, and then rises up to a height of 81 feet. Then it falls to its second bounce, and so on. Each time it falls, it bounces back to 90% of its previous height.
(a) How high does the ball rise before the 30th bounce? (Please read the question carefully. If the question read “How high does the ball rise before the second bounce?” the answer would be 81 feet.)
(b) How far has the ball traveled when it hits the ground at the 30th bounce? (Again, read carefully. If the question read “How far has the ball traveled when it hits the ground at the second bounce?” the answer would be 90 feet up plus 90 feet down plus 81 feet up plus 81 feet down, for a total of 342 feet.)
(c) How far does the ball travel in the limit as the number of bounces approaches infinity?
Homework Answers
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A ball is thrown up 90 feet in the air. it comes down, bounces,
and then...
(1 point) A ball is dropped from a height of 10 feet and bounces. Suppose that...
(1 point) A ball is dropped from a height of 10 feet and bounces. Suppose that each bounce is 5/8 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 10 ) = 6.25 feet, etc. (Assume g = 32ft/s and no air resistance.) A. Find an expression for the height, in feet, to which the ball rises after it hits the floor for the nth...
(3 points) A ball is dropped from a height of 14 feet and bounces. Suppose that...
(3 points) A ball is dropped from a height of 14 feet and bounces. Suppose that each bounce is 6/8 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 14 ) = 8.75 feet, etc. (Assume no air resistance.) A. Find an expression for the height, in feet, to which the ball rises after it hits the floor for the nth time: hm = 14(5/8^n...
(3 points) A ball is dropped from a height of 10 feet and bounces. Suppose that...
(3 points) A ball is dropped from a height of 10 feet and bounces. Suppose that each bounce is 5/8 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 10 ) = 6.25 feet, etc. (Assume no air resistance.) A. Find an expression for the height, in feet, to which the ball rises after it hits the floor for the nth time: hn = 10(5/8)^n...
5. You throw a ball straight up from the ground level to a height of 10...
5. You throw a ball straight up from the ground level to a height of 10 ft. The ball falls down and hits the floor. It then bounces back to a height that is 8 ft and repeatedly bouncing up and down indefinitely, each time reaching a height four-fifths of the previous height. (a) When the ball hits the ground the first time, we call this the first hit. Find the height of the ball on the fifth hit. (b)...
A rubber ball dropped on a hard surface takes a sequence of bounces, each one 3/5 as high as the preceding one
5. A rubber ball dropped on a hard surface takes a sequence of bounces, each one 3/5 as high as the preceding one. If this ball is dropped from a height of 15 feet, what is the total distance it has traveled after it hits the surface the fifth time? The answer is 54 and 21/125 ft, but why? A rubber ball dropped on a hard surface takes a sequence of bounces, each one 3/5 as high as the preceding...
Part 1 A ball is tossed so that it bounces off the ground, rises to a...
Part 1 A ball is tossed so that it bounces off the ground, rises to a height of 2.30 m, and then hits the ground again 1.70 m away from the first bounce. 1. How long is the ball in the air between the two bounces? 1.375 2. What is the ball's velocity in the x-direction? 3. What is the ball's speed just before the second bounce? 4. What is the angle of the velocity vector with respect to the...
suppose that you drop a ball from a window 50 meters above the ground. the ball...
suppose that you drop a ball from a window 50 meters above the ground. the ball bounces to 50% of its previous height each bounce. if the ball continues to bounce in this manner how far will it have travled up and down from the time it was dropped from the winfow until the 25th bounce?
1. Recall the following scenario from a class activity: A ba is thrown (from the ground) to a hei...
1. Recall the following scenario from a class activity: A ba is thrown (from the ground) to a height of 10 feet. It then falls and bounces repeatedly. After each bounce, it rises to of the previous height (a) Express the total vertical distance the ball travels until it stops (going up and down on each bounce) as a geometric series and compute its value using the short-cut formula for geometric series. Make sure to justify the geometric series you...
(1 point) The height f(x) (in feet) of a ball thrown by a child is f(x)...
(1 point) The height f(x) (in feet) of a ball thrown by a child is f(x) =-14x2 + 6x + 3 where x is the horizontal distance in feet from the point at which the ball is thrown. (a) How high is the ball when it leaves the child's hand? 3 (b) What is the maximum height of the balil? (c) How far from the child does the ball strike the ground? feet feet feet
A baseball is hit by the batter when the ball is 2.5 feet above the ground....
A baseball is hit by the batter when the ball is 2.5 feet above the ground. The ball leaves the bat with a velocity of 85 miles per hour at an angle of 50° above the horizontal. a. What is the maximum height of the baseball? b. When does the baseball reached its maximum height? c. If the ball does not hit anything, how many seconds is the ball in the air? d. If the ball does not hit anything,...
(1 point) A ball is dropped from a height of 10 feet and bounces. Suppose that each bounce is 5/8 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 10 ) = 6.25 feet, etc. (Assume g = 32ft/s and no air resistance.) A. Find an expression for the height, in feet, to which the ball rises after it hits the floor for the nth...
(3 points) A ball is dropped from a height of 14 feet and bounces. Suppose that each bounce is 6/8 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 14 ) = 8.75 feet, etc. (Assume no air resistance.) A. Find an expression for the height, in feet, to which the ball rises after it hits the floor for the nth time: hm = 14(5/8^n...
(3 points) A ball is dropped from a height of 10 feet and bounces. Suppose that each bounce is 5/8 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 10 ) = 6.25 feet, etc. (Assume no air resistance.) A. Find an expression for the height, in feet, to which the ball rises after it hits the floor for the nth time: hn = 10(5/8)^n...
5. You throw a ball straight up from the ground level to a height of 10 ft. The ball falls down and hits the floor. It then bounces back to a height that is 8 ft and repeatedly bouncing up and down indefinitely, each time reaching a height four-fifths of the previous height. (a) When the ball hits the ground the first time, we call this the first hit. Find the height of the ball on the fifth hit. (b)...
Part 1 A ball is tossed so that it bounces off the ground, rises to a height of 2.30 m, and then hits the ground again 1.70 m away from the first bounce. 1. How long is the ball in the air between the two bounces? 1.375 2. What is the ball's velocity in the x-direction? 3. What is the ball's speed just before the second bounce? 4. What is the angle of the velocity vector with respect to the...
1. Recall the following scenario from a class activity: A ba is thrown (from the ground) to a height of 10 feet. It then falls and bounces repeatedly. After each bounce, it rises to of the previous height (a) Express the total vertical distance the ball travels until it stops (going up and down on each bounce) as a geometric series and compute its value using the short-cut formula for geometric series. Make sure to justify the geometric series you...
(1 point) The height f(x) (in feet) of a ball thrown by a child is f(x) =-14x2 + 6x + 3 where x is the horizontal distance in feet from the point at which the ball is thrown. (a) How high is the ball when it leaves the child's hand? 3 (b) What is the maximum height of the balil? (c) How far from the child does the ball strike the ground? feet feet feet
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