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A ball is thrown straight up a 20 m/s from top of a 64 m tall building. How long does it take the ball to reach the ground

User Hania
by
9.0k points

1 Answer

4 votes

Answer:

6.2 seconds

Step-by-step explanation:

To find out how long it takes for the ball to reach the ground when thrown straight up from the top of a 64 m tall building with an initial velocity of 20 m/s, you can use the following kinematic equation:

=

+

1

2

2

h=ut+

2

1

gt

2

Where:

h is the height (negative in this case because it's falling downward, so it's -64 m),

u is the initial velocity (20 m/s),

g is the acceleration due to gravity (-9.8 m/s², taken as negative because it acts downward), and

t is the time you want to find.

Plug in the values:

64

=

(

20

)

+

1

2

(

9.8

)

2

−64=(20)t+

2

1

(−9.8)t

2

Now, rearrange and solve for

t:

64

=

20

4.9

2

−64=20t−4.9t

2

This is a quadratic equation. Rearrange it to make it equal to zero:

4.9

2

20

64

=

0

4.9t

2

−20t−64=0

Now, you can solve this quadratic equation for

t. You can use the quadratic formula:

=

±

2

4

2

t=

2a

−b±

b

2

−4ac

In this equation,

=

4.9

a=4.9,

=

20

b=−20, and

=

64

c=−64. Plug these values into the formula:

=

(

20

)

±

(

20

)

2

4

(

4.9

)

(

64

)

2

(

4.9

)

t=

2(4.9)

−(−20)±

(−20)

2

−4(4.9)(−64)

Now, calculate it:

=

20

±

400

+

1254.4

9.8

t=

9.8

20±

400+1254.4

=

20

±

1654.4

9.8

t=

9.8

20±

1654.4

Now, calculate the two possible values of

t by taking both the positive and negative square roots:

1

=

20

+

1654.4

9.8

t

1

=

9.8

20+

1654.4

2

=

20

1654.4

9.8

t

2

=

9.8

20−

1654.4

Calculating

1

t

1

:

1

20

+

40.68

9.8

60.68

9.8

6.2

seconds

t

1

9.8

20+40.68

9.8

60.68

≈6.2 seconds

Calculating

2

t

2

:

2

20

40.68

9.8

20.68

9.8

2.1

seconds

t

2

9.8

20−40.68

9.8

−20.68

≈−2.1 seconds

The negative value of

t doesn't make physical sense in this context, so we consider the positive value.

It takes approximately 6.2 seconds for the ball to reach the ground.

User Inxsible
by
8.2k points

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