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To toss a ball straight up so that it takes 4.0 seconds to return to you, it must be thrown at a speed of 19.6 meters per second. This is because it will have a speed of zero at 2.0 seconds, therefore it must have a speed of 19.6 meters per second for gravity's 9.8 meters per second squared to slow it to zero in 2 seconds.

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9y ago
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2w ago

First, determine the height the ball travels using the equation h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity, and t is the time. Since it takes 4 seconds to return to you, the total time for the round trip is 8 seconds (4 seconds up and 4 seconds down). Then, set the height when the ball is released to the height when it returns. Finally, solve for the initial velocity needed to achieve this height in 4 seconds.

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11y ago

-- You want it to rise for 2 s and then fall for 2 s .

-- You know that gravity will decrease its upward speed by 9.8 meters per second

every second that it's in the air.

-- So you have to give it an initial upward speed of 19.6 meters per second in order

for it to continue rising for the first 2 seconds, before it runs out of upward gas.

That's about 43.9 miles per hour as it leaves your hand.

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Q: What speed must you toss a ball straight up so that it takes 4 s to return to you?
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