A ball is thrown vertically upward at 20 m/s. Ignoring air resistance and considering g = -10 m/s², calculate how high it goes and the time taken to reach this height.

To find the height the ball reaches, we can use the kinematic equation:

v^2 = u^2 + 2as

where:
v = final velocity (0 m/s at the highest point)
u = initial velocity (20 m/s)
a = acceleration due to gravity (-10 m/s^2)
s = displacement (height reached)

Rearranging the equation to solve for s:

0 = (20)^2 + 2(-10)s
0 = 400 - 20s
20s = 400
s = 20 meters

Therefore, the ball reaches a height of 20 meters.

To find the time taken to reach this height, we can use the kinematic equation:

v = u + at

where:
v = final velocity (0 m/s at the highest point)
u = initial velocity (20 m/s)
a = acceleration due to gravity (-10 m/s^2)
t = time taken

Rearranging the equation to solve for t:

0 = 20 - 10t
10t = 20
t = 2 seconds

Therefore, the ball takes 2 seconds to reach a height of 20 meters.

Calculating the maximum height:

To calculate the maximum height reached by the ball, we can use the following formula:

```
v^2 = u^2 + 2as
```

where:

- v is the final velocity (0 m/s at the maximum height)
- u is the initial velocity (20 m/s)
- a is the acceleration due to gravity (-10 m/s²)
- s is the distance traveled (maximum height)

Substituting the given values into the formula, we get:

```
0^2 = 20^2 + 2(-10)s
```

Solving for s, we get:

```
s = 20 m
```

Calculating the time taken:

To calculate the time taken to reach the maximum height, we can use the following formula:

```
v = u + at
```

where:

- v is the final velocity (0 m/s at the maximum height)
- u is the initial velocity (20 m/s)
- a is the acceleration due to gravity (-10 m/s²)
- t is the time taken

Substituting the given values into the formula, we get:

```
0 = 20 - 10t
```

Solving for t, we get:

```
t = 2 s
```

Therefore, the ball goes up to a maximum height of 20 m and takes 2 seconds to reach this height.