High School Calculus Velocity question

[Noriko Kamachi]

Homework Statement

If you throw a ball straight down from a building that is 443 meters tall with a velocity of 22 m/s how long would it take to reach the ground, and what would be its speed at impact?

Homework Equations

Since the ball is being thrown down with a velocity of 22 m/s I plug that into the gravitational constant equation for Earth -4.9t^2 -22t +443.

The Attempt at a Solution

To get when the ball hits the ground I set -4.9t^2 -22t +443=0. Solving for t I get about ~7.5. To get the speed at impact I took the second derivative which is -9.8t -22. Plugging in t into this equation I get |-9.8(7.5) -22| for 95.5 m/s for the speed at impact. Was this problem handled in the correct fashion?

 

[Dick]

Homework Statement

If you throw a ball straight down from a building that is 443 meters tall with a velocity of 22 m/s how long would it take to reach the ground, and what would be its speed at impact?

Homework Equations

Since the ball is being thrown down with a velocity of 22 m/s I plug that into the gravitational constant equation for Earth -4.9t^2 -22t +443.

The Attempt at a Solution

To get when the ball hits the ground I set -4.9t^2 -22t +443=0. Solving for t I get about ~7.5. To get the speed at impact I took the second derivative which is -9.8t -22. Plugging in t into this equation I get |-9.8(7.5) -22| for 95.5 m/s for the speed at impact. Was this problem handled in the correct fashion?

It looks good to me.

 

[SteamKing]

Homework Statement

If you throw a ball straight down from a building that is 443 meters tall with a velocity of 22 m/s how long would it take to reach the ground, and what would be its speed at impact?

Homework Equations

Since the ball is being thrown down with a velocity of 22 m/s I plug that into the gravitational constant equation for Earth -4.9t^2 -22t +443.

The Attempt at a Solution

To get when the ball hits the ground I set -4.9t^2 -22t +443=0. Solving for t I get about ~7.5. To get the speed at impact I took the second derivative which is -9.8t -22. Plugging in t into this equation I get |-9.8(7.5) -22| for 95.5 m/s for the speed at impact. Was this problem handled in the correct fashion?

-9.8t-22 is not the second derivative; it's the first derivative of the position function, -4.9t²-22t+443 = 0.

 

[Noriko Kamachi]

It looks good to me.

Thanks! :D

-9.8t-22 is not the second derivative; it's the first derivative of the position function, -4.9t²-22t+443 = 0.

Ah I see! Thanks for correcting me!